MCQ (Previous Year Questions) - Function (Competition Level 1) - JEE MCQ

The range of the function f(x) 

[AIEEE-2002]

[AIEEE 2003]

Domain of definition of the function 

[AIEEE 2003]

A function f from the set of natural numbers to integers defined by   

[AIEEE 2003]

The range of the function f(x) = ^{7– x}P_x–3 is-

[AIEEE 2004]

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

[AIEEE 2004]

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

[AIEEE 2004]

The domain of the function 

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

[AIEEE-2005]

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 -

[AIEEE-2005]

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

[AIEEE 2007]

t 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

[AIEEE 2008]

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

[AIEEE 2009]

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.

[AIEEE 2009]

The domain of the function f(x) 

[AIEEE 2011]

If the function f : [1, ∞) → [1, ∞) is defined by f(x) = 2^{x(x – 1)}, then f^–1(x) is

The domain of definition of the function, y(x) given by the equation, 2^x + 2^y = 2 is    

 [JEE 2000(Scr.), 1]

The domain of definition of f(x) =

 Let E = {1, 2, 3, 4} & F = {1, 2}. Then the number of onto functions from E to F is

   Then for what value of a is f(f(x)) = x ?

(a) Suppose f(x) = (x + 1)² for x ≥– 1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y = x, then g(x) equals

[JEE. 2002 (Scr.)]

(b) Let function f : R → R be defined by f(x) = 2x + sinx for x ∈ R. Then f is

JEE. 2003 (Scr.),

 Range of the function  

Let f(x) = sinx + cosx, g (x) = x² – 1. Thus g(f(x)) is invertible for x ∈

[JEE 2004 (Scr.)]