The range of the function f(x)
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 $\{-1,1\}$.