JEE Main 2024 — Functions Questions with Solutions

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 po…

The function f: R->R, f(x)=(x²+2 x-15)/(x²-4 x+9), x R is

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…

For a differentiable function f: R → R, suppose fⁱme(x)=3 f(x)+α, where α R, f(0)=1 and x →₋∞ f(x)=7. Then 9 f (- e 3 )…

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 '…

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 =…

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 ) su…

If the domain of the function ⁻¹ ((3 x-22)/(2 x-19) )+ e ((3 x²-8 x+5)/(x²-3 x-10) ) is (α, β], then 3 α+10 β is equal…

Let f(x)=x⁵+2 x³+3 x+1, x R, and g(x) be a function such that g(f(x))=x for all x R. Then g(7)gⁱme(7) is equal to :

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