Which of the following functions is an injective (one-one) function in its respective domain? (A) `f(x) = 2x + sin 3x ` (B) `x. [x]` , (where `[.]` denotes the G.I.F) (C) `f(x)=(2^x-1)/(4^x+1)` (D) `f(x)=(2^x+1)/(4^x-1)`

Options

A. `f(x)=2x+sin 3x`
B. `f(x)=x*[x],` (where [.] denotes the G.I.F)
C. `f(x)=(2^(x)-1)/(4^(x)+1)`
D. `f(x)=(2^(x)+1)/(4^(x)-1)`

Answer

D

Explanation

`f(x)=(2^(x)+1)/(4^(x)-1)=(1)/(2^(x)-1)` is one-one function.