Question:
Find the range of the function, $f(x)=\frac{x}{|x|}$
Solution:
|x| is defined as
$|\mathrm{x}|=\mathrm{x} ; \mathrm{x}>=0$
$-\mathrm{x} ; \mathrm{x}<0$
$\frac{1}{|x|}=\frac{1}{x ;} \mathrm{x}>0$
$=\frac{-1}{x} ; \mathrm{x}<0$
$\frac{x}{|x|}=1 ; \mathrm{x}>0$
$=-1 ; \mathrm{x}<0$
Hence $f(x)$ gives output values 1 and $-1$ only.
Range is $\{1,-1\}$.
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