Question

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

(a) R − {0}
(b) R − {−1, 1}
(c) {−1, 1}
(d) None of these

Answer 1

(c) {−1, 1}

$f\left(x\right)=\frac{x}{\left|x\right|}$
$$\begin{gathered} \mathrm{Let}y=\frac{x}{\left|x\right|} \\ \mathrm{For}x>0,\left|x\right|=x \\ \Rightarrow y=\frac{x}{x}=1 \\ \mathrm{For}x<0,=-x \\ \Rightarrow y=\frac{x}{-x}=-1 \\ \mathrm{Thus},\text{r}\mathrm{ange}\mathrm{of}f\left(x\right)\mathrm{is}\{-1,1\}. \end{gathered}$$