Question

Let $f:R\to R$ where $f\left(x\right)=2^{\left|x\right|}-2^{-x}$ then $f\left(x\right)$ is

• A. periodic function
• B. one one function
• C. many one function
• D. None of these

Answer 1

The correct option is C many one function

For $x<0$

we get
$f\left(x\right)=2^{-x}-2^{-x}$

$=0$

and

For $x>0,$ we get
$f\left(x\right)=2^x-2^{-x}$

$=\frac{2^{2x}-1}{2^{-x}}$

Now $f\left(0\right)$
$=2^0-2^{-0}$
$=0$

$=f(-1),f(-2),f(-3)...f\left(n\right)$ $n\in -R_{+}$

Hence $f\left(x\right)$ is a many one function.