Question

The range of the function $f\left(x\right)=\frac{x}{|x|}$ is

Answer 1

$f\left(x\right)=\frac{x}{|x|}$

We know that

$|x|=-xin(-\infty ,0)and|x|=x\text{in}[0,\infty )$

$\text{So,}f\left(x\right)=\frac{x}{-x}=-1\text{in}(-\infty ,0)$

$\text{And}f\left(x\right)=\frac{x}{x}=1\text{in}(0,\infty )$

As clearly shown above $f\left(x\right)$ has only two values

$1$ and $-1$.

So, range of $f\left(x\right)=\{-1,1\}$

Option (C) is correct.