Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE PYQs · Mathematics · Functions

JEE Functions PYQs with Solutions

700 previous year questions from Functions (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

700 questionsMathematics2007–2026Answers + solutions

About Functions PYQs

Functions has 700 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (197) and JEE Advanced (23), spanning 2007 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 23
  • 2025: 27
  • 2024: 33
  • 2023: 35
  • 2022: 25
  • 2021: 28
  • 2020: 13
  • 2019: 15
  • 2018: 4
  • 2017: 4
  • 2016: 1
  • 2015: 1

Functions questions with solutions

1

Let ℕ denote the set of all positive integers. Consider the sets A = \ 1, 2, 3, 4, 5\ and B = \ 1, 2, 3, 4, 5, 6, 7\ . Let S be the set of all functions f: A arrow B such that

JEE Advanced 2026 Solution View → 2

Let f:(1,∞)→ℝ be a function defined as f(x) = (x-1)/(x+1) . Let f^ i+1 (x) = f(f^i(x)) , i=1, 2, …, 25 , where f^1(x)=f(x) . If g(x) + f^ 26 (x) = 0 , x ∈ (1, ∞) , then the area

JEE Main 2026 Solution View → 3

Let f be a polynomial function such that _2(f(x)) = ( _2(2+(2)/(3)+(2)/(9)+…∞))· _3(1+(f(x))/(f(1/x))) , x>0 and f(6)=37 . Then ∑_ n=1 ^ 10 f(n) is equal to ________.

JEE Main 2026 Solution View → 4

Let f: ℝ arrow ℝ be defined as f(x) = (2x^2 - 3x + 2)/(3x^2 + x + 3) . Then f is :

JEE Main 2026 Solution View → 5

Let e be the base of natural logarithm and let f: \ 1, 2, 3, 4\ arrow \ 1, e, e^2, e^3\ and g: \ 1, e, e^2, e^3\ arrow \ 1, (1)/(2), (1)/(3), (1)/(4)\ be two bijective functions

JEE Main 2026 Solution View → 6

Let f: R arrow R be a function such that f(x) + 3f((π)/(2) - x) = x , x ∈ R . Let the maximum value of f on R be α . If the area of the region bounded by the curves g(x) = x^2 and

JEE Main 2026 Solution View → 7

The sum of all the integral values of p such that the equation 3 ^2 x + 12 x - 3 = p , x ∈ ℝ , has at least one solution, is:

JEE Main 2026 Solution View → 8

Let A = \ 1, 2, 3, 4, 5, 6\ . The number of one-one functions f: A arrow A such that f(1) ≥ 3 , f(3) ≤ 4 and f(2) + f(3) = 5 , is __________.

JEE Main 2026 Solution View → 9

For the function f:[1,∞) arrow [1,∞) defined by f(x)=(x-1)^4+1 , among the two statements: (I) The set S=\ x ∈ [1,∞): f(x)=f^ -1 (x)\ contains exactly two elements, and (II) The

JEE Main 2026 Solution View → 10

Let for some α ∈ ℝ , f:ℝarrowℝ be a function satisfying f(x+y)=f(x)+2y^2+y+α xy for all x,y ∈ ℝ . If f(0)=-1 and f(1)=2 , then the value of ∑_ n=1 ^ 5 (α+f(n)) is:

JEE Main 2026 Solution View → 11

Let [·] denote the greatest integer function. If the domain of the function f(x) = ^ -1 ((4x+2[x])/(3)) is [α, β] , then 12(α + β) is equal to:

JEE Main 2026 Solution View → 12

The number of functions f: \ 1, 2, 3, 4\ arrow \ a, b, c\ , which are not onto, is:

JEE Main 2026 Solution View → 13

If the domain of the function f(x) = _ (0.6) (|(2x-5)/(x^2-4)|) is (-∞, a] ∪ \ b\ ∪ [c, d) ∪ (e, ∞) , then the value of a + b + c + d + e is _______.

JEE Main 2026 Solution View → 14

Given below are two statements: Statement I: The function f: R arrow R defined by f(x)=(x)/(1+|x|) is one-one. Statement II: The function f: R arrow R defined by f(x)= x^ 2 +4

JEE Main 2026 Solution View → 15

The sum of all the elements in the range of f(x)=Sgn( x)+Sgn( x)+Sgn( x)+Sgn( x) , x ≠ n π 2 , n ∈ Z , where Sgn ( t )= \ aligned 1, & if t>0 -1, & if t<0 aligned . , is :

JEE Main 2026 Solution View → 16

If g(x)=3 x^ 2 +2 x-3, f(0)=-3 and 4 g(f(x))=3 x^ 2 -32 x+72 , then f(g(2)) is equal to:

JEE Main 2026 Solution View → 17

Let f be a function such that 3 f(x)+2 f((m)/(19 x))=5 x, x ≠ 0 , where m=∑_ i=1 ^ 9 (i)^ 2 . Then f(5)-f(2) is equal to

JEE Main 2026 Solution View → 18

If the domain of the function f(x)= _ (10 x^ 2 -17 x+7) (18 x^ 2 -11 x+1) is (-∞, a) ∪(b, c) ∪(d, ∞)-\ e\ , then 90(a+b+c+d+e) equals:

JEE Main 2026 Solution View → 19

Consider two sets A=\ x ∈ Z:|(|x-3|-3)| ≤ 1\ and B=\ x ∈ ℝ-\ 1,2\ : ((x-2)(x-4))/(x-1) _ e (|x-2|)=0\ . Then the number of onto functions f: A arrow B is equal to

JEE Main 2026 Solution View → 20

Let the domain of the function f(x)= _ 3 _ 5 (7- _ 2 (x^ 2 -10 x+85))+ ^ -1 (|(3 x-7)/(17-x)|) be (α, β] . Then α+β is equal to :

JEE Main 2026 Solution View → 21

Let f and g be functions satisfying f(x+y)=f(x) f(y), f(1)=7 and g(x+y)=g(x y), g(1)=1 , for all x, y ∈ N . If ∑_ x=1 ^ n ( f(x) g(x) )=19607 , then n is equal to:

JEE Main 2026 Solution View → 22

If the domain of the function f(x)= ^ -1 ((5-x)/(3+2 x))+ 1 _ e (10-x) is (-∞, α] ∪[β, γ)-\ δ\ , then 6(α+β+γ+δ) is equal to

JEE Main 2026 Solution View → 23

The number of distinct real solutions of the equation x|x+4|+3|x+2|+10=0 is

JEE Main 2026 Solution View → 24

Let ℝ denote the set of all real numbers. Let a_ i , b_ i ∈ ℝ for i ∈\ 1,2,3\ . Define the functions f: ℝ arrow ℝ, g: ℝ arrow ℝ , and h: ℝ arrow ℝ by aligned & f(x)=a_1+10 x+a_2

JEE Advanced 2025 Solution View → 25

Let ℕ denote the set of all natural numbers, and ℤ denote the set of all integers. Consider the functions f: ℕ arrow ℤ and g: ℤ arrow ℕ defined by f(n)= cases (n+1) / 2 & if n is

JEE Advanced 2025 Solution View → 26

Let the domain of the function f(x)= ^ -1 ((4 x+5)/(3 x-7)) be [α, β] and the domain of g(x)= _2(2-6 _ 27 (2 x+5)) be (γ, δ) . Then |7(α+β)+4(γ+δ)| is equal to ________

JEE Main 2025 Solution View → 27

If the range of the function f(x)=(5-x)/(x^2-3 x+2) , x ≠ 1,2 , is (-∞, α] ∪[β, ∞) , then α^2+β^2 is equal to :

JEE Main 2025 Solution View → 28

Let f(x)+2 f((1)/(x))=x^2+5 and 2 g(x)-3 g((1)/(2))=x, x 0 . If α=∫_1^2 f(x) d x , and β=∫_1^2 g(x) d x , then the value of 9 α+β is:

JEE Main 2025 Solution View → 29

Let the domains of the functions f(x)= _4 _3 _7(8- _2(x^2+4 x+5)) and g(x)= ^ -1 ((7 x+10)/(x-2)) be (α, β) and [γ, δ] , respectively. Then α^2+β^2+γ^2+δ^2 is equal to :-

JEE Main 2025 Solution View → 30

Let f, ~g:(1, ∞) arrow ℝ be defined as f(x)=(2 x+3)/(5 x+2) and g(x)=(2-3 x)/(1-x) . If the range of the function f ∘ g:[2,4] arrow ℝ is [α, β] , then (1)/(β-α) is equal to

JEE Main 2025 Solution View → 31

Consider the sets A=\ (x, y) ∈ ℝ × ℝ: x^2+y^2=25\ , B=\ (x, y) ∈ ℝ × ℝ: x^2+9 y^2=144\ , C=\ (x, y) .∈ ℤ × ℤ: x^2+y^2 ≤ 4\ , and D=A ∩ B . The total number of one-one functions

JEE Main 2025 Solution View → 32

Let f: ℝ arrow ℝ be a continuous function satisfying f(0)=1 and f(2 x)-f(x)=x for all x ∈ ℝ . If _ n arrow ∞ \ f(x)-f((x)/(2^n))\ =G(x) , then ∑_ r=1 ^ 10 G(r^2) is equal to

JEE Main 2025 Solution View → 33

Let f be a function such that f(x)+3 f((24)/(x)) =4 x, x ≠ 0 . Then f(3)+f(8) is equal to

JEE Main 2025 Solution View → 34

If the domain of the function f(x)= _7(1- _4(x^2-9 x+18)) is (α, β) ∪(γ, δ) , then α+β+γ+δ is equal to

JEE Main 2025 Solution View → 35

If the domain of the function f(x)= _e((2 x-3)/(5+4 x))+ ^ -1 ((4+3 x)/(2-x)) is [α, β) then α^2+4 β is equal to

JEE Main 2025 Solution View → 36

If the domain of the function f(x)= 1 10+3 x-x^2 + 1 x+|x| is (a, b) , then (1+a)^2+b^2 is equal to :

JEE Main 2025 Solution View → 37

If the domain of the function _5(18 x-x^2-77) is (α, β) and the domain of the function _ (x-1) ((2 x^2+3 x-2)/(x^2-3 x-4)) is (γ, δ) , then α^2+β^2+γ^2 is equal to :

JEE Main 2025 Solution View → 38

Let [x] denote the greatest integer less than or equal to x . Then the domain of f(x)= ^ -1 (2[x]+1) is :

JEE Main 2025 Solution View → 39

Let f:[0,3] arrow A be defined by f(x)=2 x^3-15 x^2+36 x+7 and g:[0, ∞) arrow B be defined by g(x)= x^ 2025 x^ 2025 +1 . If both the functions are onto and S=\ x ∈ Z: x ∈ ~A or x

JEE Main 2025 Solution View → 40

Let f: R-\ 0\ arrow(-∞, 1) be a polynomial of degree 2, satisfying f(x) f((1)/(x))=f(x)+f((1)/(x)) . If f(K)=-2 K , then the sum of squares of all possible values of K is :

JEE Main 2025 Solution View → 41

Let f: ℝ arrow ℝ be a function defined by f(x)=(2+3 a) x^2+ ((a+2)/(a-1)) x+b, a ≠ 1 . If f(x+ y )=f(x)+f( y )+1- (2)/(7) x y, then the value of 28 ∑_ i=1 ^5|f(i)| is

JEE Main 2025 Solution View → 42

If f(x)= 2^x 2^x+ 2 , x ∈ ℝ , then ∑_ k=1 ^ 81 f( k 82 ) is equal to

JEE Main 2025 Solution View → 43

The number of real solution(s) of the equation x^2+3 x+2= \ |x-3|,|x+2|\ is :

JEE Main 2025 Solution View → 44

The function f:(-∞, ∞) arrow(-∞, 1) , defined by f(x)= 2^x-2^ -x 2^x+2^ -x is :

JEE Main 2025 Solution View → 45

Number of functions f:\ 1,2, …, 100\ arrow\ 0,1\ , that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ________.

JEE Main 2025 Solution View → 46

Let f: R-\ 0\ arrow R be a function such that f(x)-6 f((1)/(x))=(35)/(3 x)-(5)/(2) . If the _ x arrow 0 ((1)/(α x)+f(x))=β ; α, β ∈ R , then α+2 β is equal to

JEE Main 2025 Solution View → 47

Let f(x)= 2^ x+2 +16 2^ 2 x+1 +2^ x+4 +32 . Then the value of 8(f((1)/(15))+f((2)/(15))+…+f((59)/(15))) is equal to

JEE Main 2025 Solution View → 48

Let the range of the function f(x)=6+16 x · ((π)/(3)-x) · ((π)/(3)+x) · 3 x · 6 x, x ∈ R be [α, β] . Then the distance of the point (α, β) from the line 3 x+4 y+12=0 is :

JEE Main 2025 Solution View → 49

Let f(x)= _ e x and g(x)=(x^4-2 x^3+3 x^2-2 x+2)/(2 x^2-2 x+1) . Then the domain of f ∘ g is

JEE Main 2025 Solution View → 50

Let A=\ 1,2,3,4\ and B=\ 1,4,9,16\ . Then the number of many-one functions f: A arrow B such that 1 ∈ f(~A) is equal to :

JEE Main 2025 Solution View → 51

Let f: ℝ arrow ℝ be a function such that f(x+y)=f(x)+f(y) for all x, y ∈ ℝ , and g: ℝ arrow(0, ∞) be a function such that g(x+y)=g(x) g(y) for all x, y ∈ ℝ . If f((-3)/(5))=12 and

JEE Advanced 2024 Solution View → 52

Let f: ℝ arrow ℝ and g: ℝ arrow ℝ be functions defined by f(x)=\ array ll x|x| ((1)/(x)), & x ≠ 0, 0, & x=0, array . and g(x)= cases 1-2 x, & 0 ≤ x ≤ (1)/(2) 0, & otherwise cases

JEE Advanced 2024 Solution View → 53

Let the range of the function f(x)=(1)/(2+ 3 x+ 3 x), x ∈ ℝ be [a, b] . If α and β are respectively the A.M. and the G.M. of a and b , then (α)/(β) is equal to

JEE Main 2024 Solution View → 54

Let A=\ (x, y): 2 x+3 y=23, x, y ∈ ℕ\ and B=\ x:(x, y) ∈ A\ . Then the number of one-one functions from A to B is equal to _______

JEE Main 2024 Solution View → 55

For a differentiable function f: ℝ arrow ℝ , suppose f^ (x)=3 f(x)+α , where α ∈ ℝ , f(0)=1 and _ x arrow-∞ f(x)=7 . Then 9 f(- _ e 3) is equal to_________

JEE Main 2024 Solution View → 56

If the domain of the function f(x)= ^ -1 ((x-1)/(2 x+3)) is R-(α, β) , then 12 α β is equal to :

JEE Main 2024 Solution View → 57

If a function f satisfies f(~m+n)=f(~m)+f(n) for all m, n ∈ N and f(1)=1 , then the largest natural number λ such that ∑_ k=1 ^ 2022 f(λ+k) ≤(2022)^2 is equal to _________

JEE Main 2024 Solution View → 58

Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a] arrow[-a, a] is

JEE Main 2024 Solution View → 59

Let [t] be the greatest integer less than or equal to t . Let A be the set of all prime factors of 2310 and f: A arrow ℤ be the function f(x)=[ _2(x^2+[(x^3)/(5)])] . The number

JEE Main 2024 Solution View → 60

If the range of f(θ)=( ^4 θ+3 ^2 θ)/( ^4 θ+ ^2 θ), θ ∈ ℝ is [α, β] , then the sum of the infinite G.P., whose first term is 64 and the common ratio is (α)/(β) , is equal to________

JEE Main 2024 Solution View → 61

Let f(x)=(1)/(7- 5 x) be a function defined on R . Then the range of the function f(x) is equal to ;

JEE Main 2024 Solution View → 62

The function f: R->R, f(x)=(x^2+2 x-15)/(x^2-4 x+9), x ∈ ℝ is

JEE Main 2024 Solution View → 63

Let f, g: R arrow R be defined as : f(x)=|x-1| and g(x)= cases e^x, MARA & x ≥ 0 x+1, & x ≤ 0 cases Then the function f(g(x)) is

JEE Main 2024 Solution View → 64

Let A=\ 1,3,7,9,11\ and B=\ 2,4,5,7,8,10,12\ . Then the total number of one-one maps f: A arrow B , such that f(1)+f(3)=14 , is :

JEE Main 2024 Solution View → 65

Let f(x)=x^5+2 x^3+3 x+1, x ∈ R , and g(x) be a function such that g(f(x))=x for all x ∈ R . Then g(7) g^ (7) is equal to :

JEE Main 2024 Solution View → 66

The number of distinct real roots of the equation |x||x+2|-5|x+1|-1=0 is_______

JEE Main 2024 Solution View → 67

If S=\ a ∈ R:|2 a-1|=3[a]+2\ a\ \ , where [t] denotes the greatest integer less than or equal to t and \ t\ represents the fractional part of t , then 72 ∑_ a ∈ S a is equal to

JEE Main 2024 Solution View → 68

Consider the function f: ℝ arrow ℝ defined by f(x)= 2 x 1+9 x^2 . If the composition of f, (f ∘ f ∘ f ∘ ⋯ ∘ f) _ 10 times (x)= 2^ 10 x 1+9 α x^2 , then the value of 3 α+1 is equal

JEE Main 2024 Solution View → 69

If the domain of the function ^ -1 ((3 x-22)/(2 x-19))+ _ e ((3 x^2-8 x+5)/(x^2-3 x-10)) is (α, β] , then 3 α+10 β is equal to:

JEE Main 2024 Solution View → 70

Let the sum of the maximum and the minimum values of the function f(x)=(2 x^2-3 x+8)/(2 x^2+3 x+8) be m n , where gcd(m, n)=1 . Then m+n is equal to :

JEE Main 2024 Solution View → 71

If the domain of the function f(x) = x ^ 2 - 25 (4 - x ^ 2 ) + _ 10 ( x ^ 2 + 2x - 15) is (- ∞, α) ∪ [β, ∞), then α ^ 2 + β ^ 3 is equal to:

JEE Main 2024 Solution View → 72

Let f: R → R and g: R → R be defined as f(x) = \ cases _ e x, & x > 0 e ^ - x , & x ≤ 0 cases ) and g(x) = \ cases x, & x ≥ 0 e ^ x , & x < 0 cases ). Then, gof: R → R is:

JEE Main 2024 Solution View → 73

If the function f: (- ∞, - 1]→ (a, b)] defined by f(x) = e ^ x ^ 3 - 3x + 1 is one-one and onto, then the distance of the point P(2b + 4, a + 2) from the line x + e ^ - 3 y = 4 is:

JEE Main 2024 Solution View → 74

If f(x) = (4x + 3)/(6x - 4), x ≠ (2)/(3) and ( fof ) ( x ) = g ( x ) , where g: R - \ (2)/(3)\ → R - \ (2)/(3)\ , then ( gogog ) ( 4 ) is equal to

JEE Main 2024 Solution View → 75

If the domain of the function f(x) = _ e ( 2x + 3 4 x ^ 2 + x - 3 ) + ^ - 1 ((2x - 1)/(x + 2)) is ( α, β ] , then the value of 5β - 4α is equal to

JEE Main 2024 Solution View → 76

Let f: R → R be a function defined f(x) = x (1 + x ^ 4 ) ^ 1 / 4 and g(x) = f(f(f(f(x)))) then 18 ∫ _ 0 ^ 2 5 x ^ 2 g(x)dx

JEE Main 2024 Solution View → 77

If the domain of the function f(x) = ^ - 1 ((2 - | x |)/(4)) + ( _ e ( 3 - x )) ^ - 1 is [ - α, β ) - γ , then α + β + γ is equal to :

JEE Main 2024 Solution View → 78

Let A = 1, 2, 3, … . 7 and let P ( A ) denote the power set of A . If the number of functions f: A → P ( A ) such that a ∈ f ( a ) , ∀ a ∈ A is m ^ n , m and n ∈ N and m is least

JEE Main 2024 Solution View → 79

If f(x) = \ array ll 2 + 2x, - 1 ≤ x < 0 1 - (x)/(3), 0 ≤ x ≤ 3 array ; g(x) = \ array ll - x, - 3 ≤ x ≤ 0 x, 0 < x ≤ 1 array ), then range of ( f ∘ g ( x ) ) is

JEE Main 2024 Solution View → 80

Consider the function f: [(1)/(2), 1] → R defined by f(x) = 4 2 x ^ 3 - 3 2 x - 1 . Consider the statements (I) The curve y = f(x) intersects the x -axis exactly at one point (II)

JEE Main 2024 Solution View → 81

Let f(x) = 2 ^ x - x ^ 2 , x ∈ R . If m and n are respectively the number of points at which the curves y = f(x) and y = f ^ ' (x) intersects the x - axis, then the value of m + n

JEE Main 2024 Solution View → 82

Let f: R - \ (- 1)/(2)\ → R and g: R - \ (- 5)/(2)\ → R be defined as f(x) = (2x + 3)/(2x + 1) and g(x) = (| x | + 1)/(2x + 5) . Then the domain of the function fog is :

JEE Main 2024 Solution View → 83

The function f: N - 1 → N ; defined by f(n) = the highest prime factor of n , is :

JEE Main 2024 Solution View → 84

Let S = (0, 1) ∪ (1, 2) ∪ (3, 4) and T = \ 0, 1, 2, 3\ . Then which of the following statements is(are) true?

JEE Advanced 2023 Solution View → 85

If the domain of the function f(x) = _ e (4 x ^ 2 + 11x + 6) + ^ - 1 (4x + 3) + ^ - 1 ((10x + 6)/(3)) is ( α, β ] , then 36|α + β| is equal to

JEE Main 2023 Solution View → 86

The range of f(x) = 4 ^ - 1 ( x ^ 2 x ^ 2 + 1 ) is

JEE Main 2023 Solution View → 87

For x ∈ ℝ, two real valued functions f(x) and g(x) are such that, g ( x ) = x + 1 and fog(x) = x + 3 - x . Then f(0) is equal to

JEE Main 2023 Solution View → 88

For the differentiable function f: ℝ - 0 - ℝ, let 3f(x) + 2f((1)/(x)) = (1)/(x) - 10, then |f(3) + f ^ ' ((1)/(4))| is equal to

JEE Main 2023 Solution View → 89

Let D be the domain of the function f(x) = ^ - 1 ( _ 3x ( 6 + 2 _ 3 x - 5x )) . If the range of the function g: D → ℝ defined by g(x) = x - [x], ( [x] is the greatest integer

JEE Main 2023 Solution View → 90

The domain of the function f(x) = 1 [x] ^ 2 - 3[x] - 10 is (where [ x ] denotes the greatest integer less than or equal to x )

JEE Main 2023 Solution View → 91

Let A = \ 1, 2, 3, 4, 5\ and B = \ 1, 2, 3, 4, 5, 6\ . Then the number of functions f: A → B satisfying f(1) + f(2) = f(4) - 1 is equal to........

JEE Main 2023 Solution View → 92

If the domain of the function f(x) = sec ^ - 1 ((2x)/(5x + 3)) is [ α, β ) ∪ ( γ, δ ] , then |3α + 10 (β + γ) + 21δ| is equal to __________

JEE Main 2023 Solution View → 93

If f(x) = (tan 1 ^ ° )x + _ e (123) x _ e (1234) - (tan 1 ^ ° ) , x > 0 , then the least value of f(f(x)) + f(f((4)/(x))) is

JEE Main 2023 Solution View → 94

If domain of the function _ e ( 6 x ^ 2 + 5x + 1 2x - 1 ) + ^ - 1 ( 2 x ^ 2 - 3x + 4 3x - 5 ) is (α, β) ∪ (γ, δ), then 18 ( α ^ 2 + β ^ 2 + γ ^ 2 + δ ^ 2 ) is equal to

JEE Main 2023 Solution View → 95

Let R = a, b, c, d, e and S = 1, 2, 3, 4 . Total number of onto functions f: R → S such that f ( a ) ≠ 1 , is equal to ________.

JEE Main 2023 Solution View → 96

Let the sets A and B denote the domain and range respectively of the function f(x) = 1 [x] - x , where [x] denotes the smallest integer greater than or equal to x . Then among the

JEE Main 2023 Solution View → 97

Let 5f(x) + 4f((1)/(x)) = (1)/(x) + 3, x > 0 . Then 18 ∫ _ 1 ^ 2 f(x)dx is equal to

JEE Main 2023 Solution View → 98

Let A = x ∈ ℝ: [x + 3] + [x + 4] ≤ 3 , B = \ x ∈ ℝ: 3 ^ x ( ∑ _ r = 1 ^ ∞ 3 10 ^ r ) ^ x - 3 < 3 ^ - 3x \ , where [ t ] denotes greatest integer function. Then,

JEE Main 2023 Solution View → 99

Let f: R - \ 0, 1\ → R be a function such that f(x) + f((1)/(1 - x)) = 1 + x . Then f(2) is equal to :

JEE Main 2023 Solution View → 100

Let f: R - \ 2, 6\ → R be real valued function defined as f(x) = x + 2x + 1 x ^ 2 - 8x + 12 . Then range of f is

JEE Main 2023 Solution View → 101

If the domain of the function f(x) = [x] 1 + x ^ 2 , where [x] is greatest integer ≤ x , is [ 2, 6 ) , then its range is

JEE Main 2023 Solution View → 102

The range of the function f(x) = 3 - x + 2 + x is

JEE Main 2023 Solution View → 103

Let A = 1, 2, 3, 5, 8, 9 . Then the number of possible functions f: A → A such that f(m · n) = f(m) · f(n) for every m, n ∈ A with m · n ∈ A is equal to

JEE Main 2023 Solution View → 104

Suppose f: R → (0, ∞) be a differentiable function such that 5f(x + y) = f(x) · f(y), ∀ x, y ∈ R , If f(3) = 320 , then ∑ _ n = 0 ^ 5 f(n) is equal to:

JEE Main 2023 Solution View → 105

Let S = 1, 2, 3, 4, 5, 6 . Then the number of oneone functions f: S → P ( S ) , where P ( S ) denote the power set of S , such that f ( n ) ⊂ f ( m ) where n < m is

JEE Main 2023 Solution View → 106

Let f ^ 1 (x) = (3x + 2)/(2x + 3), x ∈ R - \ - (3)/(2)\ . For n ≥ 2 , define f ^ n (x) = f ^ 1 o f ^ n - 1 (x) . If f ^ 5 (x) = (ax + b)/(bx + a), gcd(a, b) = 1 , then a + b is

JEE Main 2023 Solution View → 107

Consider a function f: ℕ → ℝ , satisfying f(1) + 2f(2) + 3f(3) + … + xf(x) = x(x + 1)f(x); x ≥ 2 with f(1) = 1 . Then (1)/(f(2022)) + (1)/(f(2028)) is equal to

JEE Main 2023 Solution View → 108

The domain of f(x) = _ (x + 1) (x - 2) e ^ 2 _ e x - (2x + 3) , x ∈ R is

JEE Main 2023 Solution View → 109

Let f: R → R be a function such that f(x) = x ^ 2 + 2x + 1 x ^ 2 + 1 . Then

JEE Main 2023 Solution View → 110

Let f: ℝ → ℝ be a differentiable function that satisfies the relation f ( x + y ) = f ( x ) + f ( y ) - 1, ∀ x , y ∈ ℝ . If f ^ ' ( 0 ) = 2 , then | f ( - 2 ) | is equal to

JEE Main 2023 Solution View → 111

Let f: ℝ → ℝ be a function defined by f(x) = _ m \ 2 (sinx - cosx) + m - 2\ , for some m , such that the range of f is [0, 2] . Then the value of m is _____ .

JEE Main 2023 Solution View → 112

The number of functions f: 1, 2, 3, 4 → a ∈ ℤ: | a | ≤ 8 satisfying f ( n ) + (1)/(n)f ( n + 1 ) = 1, ∀ n ∈ 1, 2, 3 is

JEE Main 2023 Solution View → 113

Let f: (0, 1) → ℝ be a function defined by f(x) = 1 1 - e ^ - x , and g(x) = (f(- x) - f(x)) . Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one

JEE Main 2023 Solution View → 114

For some a, b, c ∈ ℕ , let f(x) = ax - 3 and g(x) = x ^ b + c, x ∈ ℝ . If (fog) ^ - 1 (x) = ((x - 7)/(2))(1)/(3) , then (f ∘ g)(ac) + (g ∘ f)(b) is equal to _____ .

JEE Main 2023 Solution View → 115

If f(x) = 2 ^ 2x 2 ^ 2x + 2 , x ∈ R , then f((1)/(2023)) + f((2)/(2023)) + f((3)/(2023)) . . . . . . . . . f((2022)/(2023)) is equal to

JEE Main 2023 Solution View → 116

Let f(x) be a function such that f(x + y) = f(x) · f(y) for all x, y ∈ N , If f(1) = 3 and ∑ _ k = 1 ^ n f(k) = 3279 , then the value of n is

JEE Main 2023 Solution View → 117

If f(x) = x ^ 3 - x ^ 2 f ^ ' (1) + x f ^ " (2) - f ^ ' ' ' (3) , x ∈ R , then

JEE Main 2023 Solution View → 118

The equation x ^ 2 – 4x + [ x ] + 3 = x [ x ] , where [ x ] denotes the greatest integer function, has:

JEE Main 2023 Solution View → 119

The domain of the function f(x) = ^ - 1 ( x ^ 2 - 3x + 2 x ^ 2 + 2x + 7 ) is

JEE Main 2022 Solution View → 120

Let f(x) = a x ^ 2 + bx + c be such that f(1) = 3, f(- 2) = λ and f(3) = 4 . If f(0) + f(1) + f(- 2) + f(3) = 14 , then λ is equal to

JEE Main 2022 Solution View → 121

Let α, β and γ be three positive real numbers. Let f(x) = α x ^ 5 + β x ^ 3 + , x ∈ R and g: R → R be such that g(f(x)) = x for all x ∈ R . If a _ 1 , a _ 2 , a _ 3 , … , a _ n be

JEE Main 2022 Solution View → 122

Considering only the principal values of the inverse trigonometric functions, the domain of the function f(x) = ^ - 1 ( x ^ 2 - 4x + 2 x ^ 2 + 3 ) is

JEE Main 2022 Solution View → 123

The domain of the function f(x) = ^ - 1 [2 x ^ 2 - 3] + _ 2 (log(1)/(2)( x ^ 2 - 5x + 5)) , where [t] is the greatest integer function, is

JEE Main 2022 Solution View → 124

The number of functions f , from the set A = \ x ∈ N: x ^ 2 - 10x + 9 ≤ 0\ to the set B = \ n ^ 2 : n ∈ N\ such that f(x) ≤ (x - 3) ^ 2 + 1 , for every x ∈ A , is _______.

JEE Main 2022 Solution View → 125

Let f, g: ℕ - \ 1\ → ℕ be functions defined by f(a) = α , where α is the maximum of the powers of those primes p such that p ^ α divides a , and g(a) = a + 1 , for all a ∈ ℕ - \

JEE Main 2022 Solution View → 126

Let f: R → R be a continuous function such that f(3x) - f(x) = x . If f(8) = 7 , then f(14) is equal to:

JEE Main 2022 Solution View → 127

The number of bijective function f(1, 3, 5, 7, ⋯ , 99) → (2, 4, 6, 8, ⋯ , 100) if f(3) > f(5) > f(7) ⋯ > f(99) is

JEE Main 2022 Solution View → 128

The sum of the maximum and minimum values of the function f(x) = |5x - 7| + [ x ^ 2 + 2x] in the interval [(5)/(4), 2] , where [t] is the greatest integer ≤ t , is ______.

JEE Main 2022 Solution View → 129

The total number of functions, f: \ 1, 2, 3, 4\ → \ 1, 2, 3, 4, 5, 6\ such that f(1) + f(2) = f(3) , is equal to

JEE Main 2022 Solution View → 130

Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8 x ^ 2 - 2x , and g(f(x)) = 4 x ^ 2 + 6x + 1 , then the value of f(2) + g(2) is ______.

JEE Main 2022 Solution View → 131

The domain of the function ^ - 1 ( 2 ^ - 1 ( 1 4 x ^ 2 - 1 ) π ) is

JEE Main 2022 Solution View → 132

Let c, k ∈ R . If f(x) = (c + 1) x ^ 2 + (1 - c ^ 2 )x + 2k and f(x + y) = f(x) + f(y) - xy , for all x, y ∈ R , then the value of |2(f(1) + f(2) + f(3) + … … + f(20))| is equal

JEE Main 2022 Solution View → 133

The probability that a randomly chosen one-one function from the set \ a, b, c, d\ to the set \ 1, 2, 3, 4, 5\ satisfied f(a) + 2f(b) - f(c) = f(d) is

JEE Main 2022 Solution View → 134

Let S = \ 1, 2, 3, 4\ . Then the number of elements in the set f: S × S → S: f is onto and f(a, b) = f(b, a) ≥ a ∀ (a, b) ∈ S × S is

JEE Main 2022 Solution View → 135

Let a function f: ℕ → ℕ be defined by f(n) = [ cases 2n, & n = 2, 4, 6, 8, … . . n - 1, & n = 3, 7, 11, 15, … . . (n + 1)/(2), & n = 1, 5, 9, 13, … . . cases ) then, f is

JEE Main 2022 Solution View → 136

Let S = \ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\ . Define f: S → S as f(n) = \ cases 2n, & ifn = 1, 2, 3, 4, 5 2n - 11 & ifn = 6, 7, 8, 9, 10 cases ) Let g: S ≥ S be a function such that

JEE Main 2022 Solution View → 137

Let f: R → R be a function defined f(x) = 2 e ^ 2x e ^ 2x + e . Then f((1)/(100)) + f((2)/(100)) + f((3)/(100)) + … + f((99)/(100)) is equal to ______.

JEE Main 2022 Solution View → 138

Let f: ℝ → ℝ be defined as f(x) = x - 1 and g: R → \ 1, - 1\ → ℝ be defined as g(x) = x ^ 2 x ^ 2 - 1 . Then the function fog is:

JEE Main 2022 Solution View → 139

Let f(x) = (x - 1)/(x + 1), x ∈ R - 0, - 1, 1 ) . If f ^ n + 1 (x) = f( f ^ n (x)) for all n ∈ N , then f ^ 6 (6) + f ^ 7 (7) is equal to

JEE Main 2022 Solution View → 140

Let f: N → R be a function such that f(x + y) = 2f(x)f(y) for natural numbers x and y . If f(1) = 2 , then the value of α for which ∑ _ k = 1 ^ 10 f(α + k) = (512)/(3)( 2 ^ 20

JEE Main 2022 Solution View → 141

Let f: R → R be a function defined by f(x) = (2(1 - x ^ 25 2 )(2 + x ^ 25 ))(1)/(50) . If the function g(x) = f(f(f(x))) + f(f(x)) , then the greatest integer less than or equal

JEE Main 2022 Solution View → 142

The domain of f(x) = ^ - 1 ( x ^ 2 - 5x + 6 x ^ 2 - 9 ) log( x ^ 2 - 3x + 2) is

JEE Main 2022 Solution View → 143

The number of one-one functions f: \ a, b, c, d\ → \ 0, 1, 2, … , 10\ such that 2f(a) - f(b) + 3f(c) + f(d) = 0 is _____

JEE Main 2022 Solution View → 144

The range of the function f ( x ) = _ 5 (3 + cos((3π)/(4) + x) + cos((π)/(4) + x) + cos((π)/(4) - x) - cos((3π)/(4) - x)) is :

JEE Main 2021 Solution View → 145

Let f ( x ) be a polynomial of degree 3 such that f(k) = - (2)/(k) for k = 2, 3, 4, 5 . Then the value of 52 - 10f ( 10 ) is equal to _____ .

JEE Main 2021 Solution View → 146

Let f: N → N be a function such that f(m + n) = f(m) + f(n) for every m, n ∈ N . If f(6) = 18 then f(2) · f(3) is equal to :

JEE Main 2021 Solution View → 147

The domain of the function, f(x) = ^ - 1 ( 3 x ^ 2 + x - 1 ( x - 1 ) ^ 2 ) + ^ - 1 ((x - 1)/(x + 1)) is:

JEE Main 2021 Solution View → 148

The domain of the function cosec ^ - 1 ((1 + x)/(x)) is :

JEE Main 2021 Solution View → 149

Let f: R → R be defined as f(x + y) + f(x - y) = 2f(x)f(y), f((1)/(2)) = - 1 . Then the value of ∑ _ k = 1 ^ 20 (1)/(sin(k)sin(k + f(k))) is equal to :

JEE Main 2021 Solution View → 150

Let the domain of the function f(x) = _ 4 ( _ 5 ( _ 3 (18x - x ^ 2 - 77))) be (a, b) . Then the value of the integral ∫ _ a ^ b ^ 3 x ( ^ 3 x + ^ 3 (a + b - x)) is equal to _____.

JEE Main 2021 Solution View → 151

Let S = \ 1, 2, 3, 4, 5, 6, 7\ . Then the number of possible functions f: S → S such that f(m · n) = f(m) · f(n) for every m, n ∈ S and m · n ∈ S , is equal to _____.

JEE Main 2021 Solution View → 152

If [x] be the greatest integer less than or equal to x, then ∑ _ n = 8 ^ 100 [ (- 1) ^ n n 2 ] is equal to:

JEE Main 2021 Solution View → 153

Consider function f: A → B and g: B → C(A, B, C ⊆ R) such that (gof) ^ - 1 exists, then:

JEE Main 2021 Solution View → 154

Let g: N → N be defined as g ( 3n + 1 ) = 3n + 2 g ( 3n + 2 ) = 3n + 3 g ( 3n + 3 ) = 3n + 1 , for all n ≥ 0 Then which of the following statements is true ?

JEE Main 2021 Solution View → 155

Let [x] denote the greatest integer less than or equal to x . Then, the values of x ∈ R satisfying the equation [ e ^ x ] ^ 2 + [ e ^ x + 1] - 3 = 0 lie in the interval:

JEE Main 2021 Solution View → 156

If the domain of the function f(x) = ^ - 1 x ^ 2 - x + 1 ^ - 1 ((2x - 1)/(2)) is the interval ( α, β ] , then α + β is equal to:

JEE Main 2021 Solution View → 157

Let A = 0, 1, 2, 3, 4, 5, 6, 7 . Then the number of bijective functions f: A → A such that f ( 1 ) + f ( 2 ) = 3 - f ( 3 ) is equal to

JEE Main 2021 Solution View → 158

Let f: R - \ (α)/(6)\ → R be defined by f(x) = ((5x + 3)/(6x - α)) . Then the value of α for which (fof)(x) = x , for all x ∈ R - \ (α)/(6)\ , is

JEE Main 2021 Solution View → 159

Let [x] denote the greatest integer ≤ x , where x ∈ R . If the domain of the real valued function f(x) = (|[x]| - 2)/(|[x]| - 3) is (- ∞ , a) ∪ [b, c) ∪ [4, ∞), a < b < c , then

JEE Main 2021 Solution View → 160

Let f: R - 3 → R - 1 be defined by f(x) = (x - 2)/(x - 3) . Let g: R → R be given as g ( x ) = 2x - 3 . Then, the sum of all the values of x for which f ^ - 1 (x) + g ^ - 1 (x) =

JEE Main 2021 Solution View → 161

The real valued function f(x) = cosec ^ - 1 x x - [ x ] , where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to:

JEE Main 2021 Solution View → 162

If the functions are defined as f ( x ) = x and g ( x ) = 1 - x , then what is the common domain of the following functions: f + g, f - g, f / g, g / f, g - f , where (f ± g)(x) =

JEE Main 2021 Solution View → 163

The inverse of y = 5 ^ logx is:

JEE Main 2021 Solution View → 164

The number of elements in the set \ x ∈ R: (| x | - 3)|x + 4| = 6\ is equal to

JEE Main 2021 Solution View → 165

Let A = \ 1, 2, 3, … , 10\ and f: A → A be defined as f(k) = \ cases k + 1 & ifkis odd k & ifkis even cases ) Then the number of possible functions g: A → A such that gof = f is:

JEE Main 2021 Solution View → 166

Let f(x) = ^ - 1 x and g(x) = x ^ 2 - x - 2 2 x ^ 2 - x - 6 . If g(2) = _ x → 2 g(x) , then the domain of the function fog is

JEE Main 2021 Solution View → 167

A function f ( x ) is given by f(x) = 5 ^ x 5 ^ x + 5 , then the sum of the series f((1)/(20)) + f((2)/(20)) + f((3)/(20)) + … + f((39)/(20)) is equal to:

JEE Main 2021 Solution View → 168

Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the

JEE Main 2021 Solution View → 169

Let f, g: N → N such that f(n + 1) = f(n) + f(1) ∀ n ∈ N and g be any arbitrary function. Which of the following statements is NOT true?

JEE Main 2021 Solution View → 170

If a + α = 1, b + β = 2 and af(x) + ((1)/(x)) = bx + (β)/(x), x ≠ 0, then the value of the expression (f(x) + f((1)/(x)))/(x + (1)/(x)) is ___________.

JEE Main 2021 Solution View → 171

Let f: R → R be defined as f(x) = 2x - 1 and g: R - \ 1\ → R . be defined as g(x) = (x - (1)/(2))/(x - 1) . Then the composition function f(g(x)) is:

JEE Main 2021 Solution View → 172

Let the function f: [0, 1] → ℝ be defined by f(x) = 4 ^ x 4 ^ x + 2 . Then the value of f((1)/(40)) + f((2)/(40)) + f((3)/(40)) + ⋯ + f((39)/(40)) - f((1)/(2)) is_________

JEE Advanced 2020 Solution View → 173

If the function f: R → R is defined by f(x) = |x|(x - sinx) , then which of the following statements is TRUE?

JEE Advanced 2020 Solution View → 174

For a suitably chosen real constant a , let a function, f: R - \ - a\ → R be defined by f(x) = (a - x)/(a + x) . Further supposed that for any real number x ≠ - a, and f ( x ) ≠

JEE Main 2020 Solution View → 175

Suppose that a function f: R → R satisfies f(x + y) = f(x)f(y) for all x, yεR and f(1) = 3 . If ∑ _ i = 1 ^ n f(i) = 363 , then n is equal to ..... .

JEE Main 2020 Solution View → 176

If f ( x + y ) = f ( x ) f ( y ) and Σ _ x = 1 ^ ∞ f(x) = 2, x, y ∈ N , where N is the set of all natural numbers, then the value of (f ( 4 ))/(f ( 2 )) is

JEE Main 2020 Solution View → 177

Let A = a, b, c and B = 1, 2, 3, 4 . Then the number of elements in the set C = f: A → B ∣ 2 ∈ f ( A ) and f is not one-one is …

JEE Main 2020 Solution View → 178

The minimum value of 2 ^ sinx + 2 ^ cosx is :

JEE Main 2020 Solution View → 179

Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + x y ^ 2 + x ^ 2 y, for all real x and y . If _ x → 0 (f(x))/(x) = 1, then f ^ ' (3) is equal

JEE Main 2020 Solution View → 180

Let f: R → R be a function which satisfies f(x + y) = f(x) + f(y), ∀ x, y ∈ R . If f(1) = 2 and g(n) = ∑ _ k = 1 ^ (n - 1) f(k), n ∈ N then the value of n , for which g(n) = 20

JEE Main 2020 Solution View → 181

The domain of the function f ( x ) = ^ - 1 ( |x| + 5 x ^ 2 + 1 ) is (- ∞ , - a] ∪ [a, ∞) , then a is equal to

JEE Main 2020 Solution View → 182

Let f: (1, 3) → R , be a function defined by f(x) = x[x] 1 + x ^ 2 , where [x] , denotes the greatest integer ≤ x . Then the range of f , is

JEE Main 2020 Solution View → 183

The inverse function of f(x) = 8 ^ 2x - 8 ^ - 2x 8 ^ 2x + 8 ^ - 2x , x ∈ (- 1, 1), is __________.

JEE Main 2020 Solution View → 184

If g(x) = x ^ 2 + x - 1 and (gof)(x) = 4 x ^ 2 - 10x + 5, then f((5)/(4)) is equal to

JEE Main 2020 Solution View → 185

For x ∈ R, Let [ x ] denotes the greatest integer ≤ x, then the sum of the series [- (1)/(3)] + [- (1)/(3) - (1)/(100)] + [- (1)/(3) - (2)/(100)] + . . . . . + [- (1)/(3)

JEE Main 2019 Solution View → 186

For xϵ ( 0, (3)/(2) ) , let f(x) = x , g(x) = tanx and h(x) = 1 - x ^ 2 1 + x ^ 2 . If ϕ(x) = ( hof ) og ) ( x ) , then ϕ((π)/(3)) is equal to:

JEE Main 2019 Solution View → 187

Let f(x) = _ e (sinx), (0 < x < π) and g(x) = ^ - 1 ( e ^ - x ), ( x ≥ 0 ) . If α is a positive real number such that a = (fog) ^ ' ( α ) and b = (fog) ( α ) , then

JEE Main 2019 Solution View → 188

Let f(x) = x ^ 2 , x ∈ R . For any A ⊆ R, define g(A) = x ∈ R: f ( x ) ∈ A . If S = [ 0, 4 ] , then which one of the following statements is not true?

JEE Main 2019 Solution View → 189

The domain of the definition of the function f(x) = 1 4 - x ^ 2 + _ 10 ( x ^ 3 - x) is:

JEE Main 2019 Solution View → 190

If the function f: R - \ 1, - 1\ → A defined by f(x) = x ^ 2 1 - x ^ 2 , is surjective, then A is equal to

JEE Main 2019 Solution View → 191

Let f(x) = a ^ x ( a > 0 ) be written as f(x) = f _ 1 (x) + f _ 2 (x), where f _ 1 ( x ) is an even function and f _ 2 ( x ) is an odd function. Then f _ 1 (x + y) + f _ 1 ( x - y

JEE Main 2019 Solution View → 192

If f(x) = _ e ((1 - x)/(1 + x)), |x| < 1, then f( 2x 1 + x ^ 2 ) is equal to

JEE Main 2019 Solution View → 193

Let a function f:(0, ∞) arrow(0, ∞) be defined by f(x)=|1-(1)/(x)| . Then f is :

JEE Main 2019 Solution View → 194

The number of functions f from \ 1,2,3, …, 20\ onto \ 1,2,3, …, 20\ such that f(k) is a multiple of 3, whenever k is a multiple of 4 is:

JEE Main 2019 Solution View → 195

Let f: R arrow R be defined by f(x)= x 1+x^ 2 , x ∈ R . Then the range of f is

JEE Main 2019 Solution View → 196

Let N be the set of natural numbers and two functions f and g be defined as f, g: N → N such that f(n) = \ array ll (n + 1)/(2), ifnisodd (n)/(2), ifniseven array ) and g(n) = n

JEE Main 2019 Solution View → 197

Let f: [0,1] → R be such that f(xy) = f(x) . f(y), for all x, y ∈ [0,1], and f ( 0 ) ≠ 0 . If y = y ( x ) satisfies the differential equation, (dy)/(dx) = f(x) with y(0) = 1 then

JEE Main 2019 Solution View → 198

Let A = x ∈ R: x is not a positive integer . Define a function f: A → R as f(x) = (2x)/(x - 1) , then f is:

JEE Main 2019 Solution View → 199

For x ∈ R - \ 0, 1\ , let f _ 1 (x) = (1)/(x), f _ 2 (x) = 1 - x and f _ 3 (x) = (1)/(1 - x) be three given functions. If a function, J(x) satisfies ( f _ 2 oJo f _ 1 ) (x) = f _

JEE Main 2019 Solution View → 200

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of one-one functions from X → Y and β is the number of onto functions from Y → X

JEE Advanced 2018 Solution View →
Practice all Functions questions in the app →

Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)Determinants (508)

Functions in other exams

NDA Functions (129)BITSAT Functions (39)