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Functions — JEE Main & Advanced Mathematics PYQs

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

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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 B such that f(2) 2 and f(4)

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) + f²⁶(x) = 0 , x (1, ) , then the area of the region

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 ¹⁰f(n) is equal to ________.

JEE Main 2026 Solution View → 4

Let f: R 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 1, e, e^2, e^3 and g: 1, e, e^2, e^3 1, 1 2 , 1 3 , 1 4 be two bijective functions such that f is strictly decreasing a

JEE Main 2026 Solution View → 6

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

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 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, ) [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 set S= x [1, ):

JEE Main 2026 Solution View → 10

Let for some R , f: R R be a function satisfying f(x+y)=f(x)+2y^2+y+ xy for all x,y R . If f(0)=-1 and f(1)=2 , then the value of _ n=1 ⁵( +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 [ , ] , then 12( + ) is equal to:

JEE Main 2026 Solution View → 12

The number of functions f: 1, 2, 3, 4 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 R defined by f(x)= x 1+|x| is one-one. Statement II: The function f: R R defined by f(x)= x²+4 x-30 x²-8 x+18 is many

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 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 x²+2 x-3, f(0)=-3 and 4 g(f(x))=3 x²-32 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 x²-17 x+7 ) (18 x²-11 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 B is equal to

JEE Main 2026 Solution View → 20

Let the domain of the function f(x)= ₃ ₅ (7- ₂ (x²-10 x+85 ) )+ ⁻¹ ( | 3 x-7 17-x | ) be ( , ] . Then + 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 (- , ] [ , )- , then 6( + + + ) 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 R , g: R R , and h: R R by aligned & f(x)=a₁+10 x+a₂ x^2+a₃ x^3+x^4, & g(x)=b₁+3

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 Z and g: Z N defined by f(n)= cases (n+1) / 2 & if n is odd (4-n) / 2

JEE Advanced 2025 Solution View → 26

Let the domain of the function f(x)= ⁻¹ ( 4 x+5 3 x-7 ) be [ , ] and the domain of g ( x )= ₂ (2-6 ₂₇(2 x +5) ) be ( , ) . Then |7( + )+4( + )| 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 (- , ] [ , ) , then ^2+ ^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 = ₁^2 f(x) d x , and = ₁^2 g(x) d x , then the value of 9 + 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 ( , ) and [ , ] , respectively. Then ^2+ ^2+ ^2+ ^2 is equal to :-

JEE Main 2025 Solution View → 30

Let f, ~g :(1, ) 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] R is [ , ] , then 1 - 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 from

JEE Main 2025 Solution View → 32

Let f: R R be a continuous function satisfying f(0)=1 and f(2 x )-f( x )= x for all x R . If _ n 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 ( , ) ( , ) , then + + + 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 [ , ) then ^2+4 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 ( , ) and the domain of the function _ (x-1) ( 2 x^2+3 x-2 x^2-3 x-4 ) is ( , ) , then ^2+ ^2+ ^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] A be defined by f(x)=2 x^3-15 x^2+36 x+7 and g:[0, ) B be defined by g (x)= x²⁰²⁵ x²⁰²⁵+1 . If both the functions are onto and S = x Z : x ~A or x ~B , then n ( S ) is

JEE Main 2025 Solution View → 40

Let f: R - 0 (- , 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 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:(- , ) (- , 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 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 R be a function such that f(x)-6 f ( 1 x )= 35 3 x - 5 2 . If the _ x 0 ( 1 x +f(x) )= ; , R , then +2 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 ( 3 -x ) ( 3 +x ) 3 x 6 x, x R be [ , ] . Then the distance of the point ( , ) 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 B such that 1 f( ~A ) is equal to :

JEE Main 2025 Solution View → 51

Let f: R R be a function such that f(x+y)=f(x)+f(y) for all x, y R , and g: R (0, ) be a function such that g(x+y)=g(x) g(y) for all x, y R . If f ( -3 5 )=12 and g ( -1 3 )=2 , th

JEE Advanced 2024 Solution View → 52

Let f: R R and g: R 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 Let a, b, c, d R . Define

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 and are respectively the A.M. and the G.M. of a and b , then 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 R , suppose f^ (x)=3 f(x)+ , where R , f(0)=1 and _ x - 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 -( , ) , then 12 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 such that _ k=1 ²⁰²² f( +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] [-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 Z be the function f(x)= [ ₂ (x^2+ [ x^3 5 ] ) ] . The number of one

JEE Main 2024 Solution View → 60

If the range of f( )= ^4 +3 ^2 ^4 + ^2 , R is [ , ] , then the sum of the infinite G.P., whose first term is 64 and the common ratio is , 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 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 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 R defined by f(x)= 2 x 1+9 x^2 . If the composition of f, (f f f f) _ 10 times (x)= 2¹⁰ x 1+9 x^2 , then the value of 3 +1 is equal to ______

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 ( , ] , then 3 +10 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 + log 10 x 2 + 2 x − 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 = log e x , x > 0 e − x , x ≤ 0 and g x = x , x ≥ 0 e x , x < 0 . Then, g o f : R → R is:

JEE Main 2024 Solution View → 73

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

JEE Main 2024 Solution View → 74

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

JEE Main 2024 Solution View → 75

If the domain of the function f x = log e 2 x + 3 4 x 2 + x - 3 + cos - 1 2 x - 1 x + 2 is ( α , β ] , then the value of 5 β - 4 α 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 d x

JEE Main 2024 Solution View → 77

If the domain of the function f x = cos - 1 2 - | x | 4 + log 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 = 2 + 2 x , - 1 ≤ x < 0 1 - x 3 , 0 ≤ x ≤ 3 ; g x = - x , - 3 ≤ x ≤ 0 x , 0 < x ≤ 1 , 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) The curv

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 is

JEE Main 2024 Solution View → 82

Let f : R - - 1 2 → R and g : R - - 5 2 → R be defined as f x = 2 x + 3 2 x + 1 and g x = | x | + 1 2 x + 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 &#8746; 1 , 2 &#8746; 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 = log e 4 x 2 + 11 x + 6 + sin - 1 4 x + 3 + cos - 1 10 x + 6 3 is ( &#945; , &#946; ] , then 36 &#945; + &#946; is equal to

JEE Main 2023 Solution View → 86

The range of f x = 4 sin - 1 x 2 x 2 + 1 is

JEE Main 2023 Solution View → 87

For x &#8712; &#8477; , two real valued functions f x and g x are such that, g ( x ) = x + 1 and f o g x = x + 3 - x . Then f 0 is equal to

JEE Main 2023 Solution View → 88

For the differentiable function f : &#8477; - 0 - &#8477; , let 3 f x + 2 f 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 = sin - 1 log 3 x 6 + 2 log 3 x - 5 x . If the range of the function g : D &#8594; &#8477; defined by g x = x - x , ( x is the greatest inte

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 &#8594; 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 2 x 5 x + 3 is [ &#945; , &#946; ) &#8746; ( &#947; , &#948; ] , then 3 &#945; + 10 &#946; + &#947; + 21 &#948; is equal to __________

JEE Main 2023 Solution View → 93

If f x = tan 1 &#176; x + log e 123 x log e 1234 - tan 1 &#176; , x &#62; 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 log e 6 x 2 + 5 x + 1 2 x - 1 + cos - 1 2 x 2 - 3 x + 4 3 x - 5 is &#945; , &#946; &#8746; &#947; , &#948; , then 18 &#945; 2 + &#946; 2 + &#947; 2 + &#94

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 &#8594; S such that f ( a ) &#8800; 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 state

JEE Main 2023 Solution View → 97

Let 5 f x + 4 f 1 x = 1 x + 3 , x &#62; 0 . Then 18 &#8747; 1 2 f x d x is equal to

JEE Main 2023 Solution View → 98

Let A = x &#8712; &#8477; : x + 3 + x + 4 &#8804; 3 , B = x &#8712; &#8477; : 3 x &#8721; r = 1 &#8734; 3 10 r x - 3 &#60; 3 - 3 x , where [ t ] denotes greatest integer function.

JEE Main 2023 Solution View → 99

Let f : R - 0 , 1 &#8594; 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 &#8594; R be real valued function defined as f x = x + 2 x + 1 x 2 - 8 x + 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 &#8804; 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 &#8594; A such that f m &#183; n = f m &#183; f n for every m , n &#8712; A with m &#183; n &#8712; A is

JEE Main 2023 Solution View → 104

Suppose f : R &#8594; 0 , &#8734; be a differentiable function such that 5 f x + y = f x &#183; f y , &#8704; x , y &#8712; R , If f 3 = 320 , then &#8721; 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 &#8594; P ( S ) , where P ( S ) denote the power set of S , such that f ( n ) &#8834; f ( m ) where n &#60

JEE Main 2023 Solution View → 106

Let f 1 x = 3 x + 2 2 x + 3 , x &#8712; R - - 3 2 . For n &#8805; 2 , define f n x = f 1 o f n - 1 x . If f 5 x = a x + b b x + a , gcd a , b = 1 , then a + b is equal to ________

JEE Main 2023 Solution View → 107

Consider a function f : &#8469; &#8594; &#8477; , satisfying f 1 + 2 f 2 + 3 f 3 + &#8230; + x f x = x x + 1 f x ; x &#8805; 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 = log x + 1 x - 2 e 2 log e x - 2 x + 3 , x &#8712; R is

JEE Main 2023 Solution View → 109

Let f : R &#8594; R be a function such that f x = x 2 + 2 x + 1 x 2 + 1 . Then

JEE Main 2023 Solution View → 110

Let f : &#8477; &#8594; &#8477; be a differentiable function that satisfies the relation f ( x + y ) = f ( x ) + f ( y ) - 1 , &#8704; x , y &#8712; &#8477; . If f ' ( 0 ) = 2 , th

JEE Main 2023 Solution View → 111

Let f : &#8477; &#8594; &#8477; be a function defined by f x = log m 2 sin x - cos x + 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 &#8594; a &#8712; &#8484; : | a | &#8804; 8 satisfying f ( n ) + 1 n f ( n + 1 ) = 1 , &#8704; n &#8712; 1 , 2 , 3 is

JEE Main 2023 Solution View → 113

Let f : 0 , 1 &#8594; &#8477; 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-on

JEE Main 2023 Solution View → 114

For some a , b , c &#8712; &#8469; , let f x = a x - 3 and g x = x b + c , x &#8712; &#8477; . If f o g - 1 x = x - 7 2 1 3 , then f &#8728; g a c + g &#8728; f b is equal to _____

JEE Main 2023 Solution View → 115

If f x = 2 2 x 2 2 x + 2 , x &#8712; 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 &#183; f y for all x , y &#8712; N , If f 1 = 3 and &#8721; 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 &#34; 2 - f ' ' ' 3 , x &#8712; R , then

JEE Main 2023 Solution View → 118

The equation x 2 &#8211; 4 x + [ 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 = sin - 1 x 2 - 3 x + 2 x 2 + 2 x + 7 is

JEE Main 2022 Solution View → 120

Let f x = a x 2 + b x + c be such that f 1 = 3 , f - 2 = &#955; and f 3 = 4 . If f 0 + f 1 + f - 2 + f 3 = 14 , then &#955; is equal to

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