MCQ (Previous Year Question) - Relations And Functions (Competition Level 1) - JEE MCQ

The range of the function f(x) = , x > 2 is-  

The function f(x) = log (x + ), is-         

Domain of definition of the function f(x) = + log₁₀ (x³ – x), is- 

If f : R → R satisfies f(x+ y) = f(x) + f(y), for all x, y Î R and f(1) = 7, then is- 

A function f from the set of natural numbers to integers defined by f(n) = is   

The range of the function f(x) = ^7xP_x3 is- 

If f : R → S, defined by f(x) = sin x – √3cos x+ 1, is onto, then the interval of S is-

The graph of the function y = f(x) is symmetrical about the line x = 2, then- 

The domain of the function f(x) = is-

Let f : (–1, 1) → B, be a function defined by f(x) = tan^-1 , then f is both one-one and onto when B is the interval - 

A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y)– f (a–x) f(a + y) where a is a given constant and f(0)=1, then f(2a – x) is equal to -

The largest interval lying in  for which the function  is defined, is - 

Let f : N → Y be a function defined as f(x) = 4x + 3 where Y = |y ∈ N : y = 4x + 3 for some x ∈ N|. Show that f is invertible and its inverse is  

For real x, let f(x) = x³ + 5x + 1, then - 

Let f(x) = (x + 1)² –1, x > –1 
Statement – 1 : The set {x : f(x) = f^-1(x)} = {0, - 1}.
Statement – 2 : f is a bijection.

The domain of the function f(x) =  is :