Question:
The range of the function $f(x)=\frac{x}{|x|}$ is
(a) R − {0}
(b) R − {−1, 1}
(c) {−1, 1}
(d) None of these
Solution:
(c) {−1, 1}
$f(x)=\frac{x}{|x|}$
Let $y=\frac{x}{|x|}$
For $x>0,|x|=x$
$\Rightarrow y=\frac{x}{x}=1$
For $x<0,=-x$
$\Rightarrow y=\frac{x}{-x}=-1$
Thus, r ange of $f(x)$ is $\{-1,1\}$.