Test: Relations & Functions- 4 - JEE MCQ

The function f(x) = log (1+x/1-x) satisfies the equation

If f(x + y + z) = f(x) f(y) f(z) for all x , y z and if f(2) = 4, f’(0) = 5 and f(0) ≠ 0, then f’(2) is equal to

The domain of the function

If A = {(x, y) : x²+y² = 5} and B = {(x, y) : 2x = 5y}, then A∩B contains

If f : R → R is given by f(x) = |x| and A = {x∈R:x<0}, then f^-1 (A) equals

If f : N × N →N is such that f (m, n) = m + n where N is the set of natural number, then which of the following is true ?

The function (sin x/3) is periodic with period

If A = [a, b], B = [c,d], C = [d, e] then {(a, c), (a, d), (a,e), (b,c), (b, d), (b, e)} is equal to

The function f(x) = 10^x from R to [0, ∞) is

For all x ∈ (0, 1)

The domain of the function 

Let f (x) = x² and g (x) = √x, then

Suppose that g (x) = 1+ √x and f(g(x)) = 3 + 2 √x + x, then f (x) is

The number of elements in the Power set P(S) of the set S = [[Φ], 1, [2, 3]] is

The minimum value of (x - α) (x – β) is

If f(x) = (25 - x⁴)^1/4 for 0 < x < √5, then f(f(1/2)) =

Two functions f:R→R g : R→Rare defined as follows :

 then (gof)(e) + (fog)(π) = 

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

Coefficient of x³ in the expansion of tan x is

 then (fof) (2) is equal to

If f(x) = log (1+x/1-x), then f(x) is