JEE Advanced Level Test: Relations and Functions- 1 - JEE MCQ

Find domain of the function f(x) = 

The domain of the function  is (where [x] denotes greatest integer function)

Range of f(x) = 4^x + 2^x + 1 is

Range of f(x) = log_√5 {√2 (sin x –cos x) + 3} is

The range of the functin f(x) = log_√2(2– log₂ (16 sin² x + 1)) is

Range of the function f(x)= is

If f(x) = , then range of f(x) is

The sum  is equal to (where [*] denotes the greatest integer function)

Which of the following represents the graph of f(x) = sgn ([x + 1])

If f(x) = 2 sin²q+4 cos (x+q) sin x. sin q+cos (2x+2q) then value of f²(x) + f²  is

Let f(x) = ax² + bx + c, where a, b, c are rational and f : Z → Z, where Z is the set of integers. Then a+ b is

Which one of the following pair of functions are identical ?

The function f : [2, ∞) → Y defined by f(x) = x² – 4x + 5 is both one–one & onto if

Let f : R → R be a function defined by f(x) =  then f is

Let f : R → R be a function defined by f(x) = x³ + x² + 3x + sin x. Then f is

If f(x) = x³ + (a – 3) x² + x + 5 is a one–one function, then

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

The function f : R → R defined by f(x) = 6^x + 6^|x| is

Let `f' be a function from R to R given by f(x) = . Then f(x) is

If f(x) = cot^-1 x : R⁺ →  and g(x) = 2x – x² : R → R. Then the range of the function f(g(x)) wherever define is

Let g(x) = 1 + x – [x] and f(x) = , then  x, fog(x) equals (where [*] represents greatest integer function).

Let f: [0, 1] → [1, 2] defined as f(x) = 1 + x and g : [1, 2] → [0, 1] defined as g(x) = 2 – x then the composite function gof is

Let f & g be two functions both being defined from R → R as follows f(x) =  and g(x) = . Then

If y = f (x) satisfies the condition f = x² +  (x > 0) then f(x) equals

The function f(x) = log  is

It is given that f(x) is an even function and satisfy the relation f(x) = then the value of f(10) is

Fundamental period of f(x) = sec (sin x) is