JEE Main 2019 — Functions Questions with Solutions

For x ∈ R ,   Let [ x ] denotes the greatest integer ≤ x ,   then the sum of the series - 1 3 + -…

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…

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 mu…

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

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

Let f : 0,1 → R   be such that f x y = f x . f y , for all x , y ∈ 0,1 ,   and   f ( 0 ) &#8…

Let f x = x 2 ,   x ∈ R . For any A ⊆ R , define g A = { x ∈ R   : f ( x ) ∈ A } . If…

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 fun…

Let A =   { x ∈ R : x is not a positive integer} . Define a function   f : A → R as f x = 2 x x -…

For x   ϵ   ( 0 , 3 2 ) , let f x = x , g x = t a n x and h x = 1 - x 2 1 + x 2 . If ϕ x = ( h o f…