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Functions — BITSAT Mathematics PYQs

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

Functions — BITSAT Mathematics PYQs

Let [x] denote the greatest integer x . If f(x)=[x] and g(x)=|x| , then the value of f (g ( 8 5 ) )-g (f (- 8 5 ) ) is

Number of real solution of 5- ₂|x| =3- ₂|x| is equal to

f(x)= x [ 2 x ]+ 1 2 , where x is not an integral multiple of and [.] denotes the greatest integer function, is

The function f: R R defined by f(x)= x 1+x^2 is

If f: R R, g: R R are defined by f(x)=5 x-3, g(x)=x^2+3 , then g o f⁻¹(3) is equal to

The domain of the real valued function f(x)= 2 x^2-7 x+5 3 x^2-5 x-2 is

If a function f : R - l R - m defined by f(x)= x+3 x-2 is a bijection, then 3 l+2 m=

f(x)= x+ x, g(x)=x^2-1 , then g(f(x)) is invertible if

Let the function g:(- , ) (- 2 , 2 ) be given by g(u)=2 ⁻¹ (e^u )- 2 . Then, g is

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

Consider the function f in A = R - 2 3 defined as f(x)= 4 x+3 6 x-4 , then f⁻¹ is equal to

If f(x)= x 1+x^2 , then (fof of) (x) is

If g(x)=x^2+x-2 and 1 2 g o f(x)=2 x^2-5 x+2 then f(x) is equal to

The domain of the function f (x)= 1 x¹²-x⁹+x⁴-x+1 is given by

Let [x] denote the greatest integer x . If f(x)=[ x ] and g(x)=|x|, then the value of f ( g ( 8 5 ) )- g ( f (- 8 5 ) ) is

The domain of the function f(x)= x- 1-x² is

Number of solution of the equation | cos x | = 2 [ x ] are (where | x | , [ x ] are modulus and greatest integer function respectively).

The inverse of the function f x = log a x + x 2 + 1 (where, a &#60; 0 , a &#8800; 1 ) is

Let f : R &#8594; R be a function satisfying f x + y = f x + 2 y 2 + k x y for all x , y &#8712; R . If f 1 = 2 and f 2 = 8 , then f x is equal to

Let A = - 1 , 1 and f : A &#8594; A be defined as f x = x x for all x &#8712; A , then f x is

If a function f : R &#8594; R satisfy the equation f ( x + y ) = f ( x ) + f ( y ) , &#8704; x , y and the function f ( x ) is continuous at x = 0 , then

Let f(x)= a x+b c x+d , then fof (x)=x, provided that:

Match List I with List II and select the correct answer using the code given below the lists: ( array l|l List I & List II (A) f(x)= x & 1. The graph cuts y-axis in infinite number

The period of 3 is

The domain of the function f(x)= ⁻¹(x-3) 9-x²

The domain of the function f(x)= ₂ (- _ 1 / 2 (1+ 1 x^ 1 / 4 )-1 ) is

Let f : R R be a function defined by f(x)= x-m x-n , where m n, then

If f is an even function and g is an odd function, then the function fog is

If (f(x) ) is a function that is odd and even simultaneously, then ( f (3)- f (2) ) is equal to

If (f(x)= array l x ; when x is rational 1-x ; when x is irrational array . ), then fof ((x) ) is given as

If (f(x)= 1-x 1+x ) the domain of (f⁻¹(x) ) is

A black die and a white die are rolled. Find the probability that the number shown by the black die will be more than twice that shown by the white die.

Let (E= 1,2,3,4 ) and (F= 1,2 ). Then the number of onto functions from ( E ) to ( F ) is

The range of the function (f(x)= x^2-x+1 x^2+x+1 ) where ( x R ), is

If ( ( z ₁ )= (z₂ ) ), then

Find the vertex of the parabola (x^2-8 y-x+19=0 ).

Given below is a frequency distribution with median 46 . In this distribution, some of the frequencies are missing : Determine the missing frequencies. ( array |c|c|c|c|c|c|c|c|c|

If (y=e^ -x x ) and (y₄+k y=0 ), where (y₄= d^4 y d x^4 ), then (k= )

The value of ( _ x 0 (4^x-1 )^3 x^2 4 (1+3 x) ), is

The inverse of the function f x = log a x + x 2 + 1 (where, a < 0 , a ≠ 1 ) is

Let f : R → R be a function satisfying f x + y = f x + 2 y 2 + k x y for all x , y ∈ R . If f 1 = 2 and f 2 = 8 , then f x is equal to

Let A = - 1 , 1 and f : A → A be defined as f x = x x for all x ∈ A , then f x is

If a function f : R → R satisfy the equation f ( x + y ) = f ( x ) + f ( y ) , ∀ x , y and the function f ( x ) is continuous at x = 0 , then