Question:
The range of the function $f(x)=\frac{|x-4|}{x-4}$ is ______ .
Solution:
$f(x)=\frac{|x-4|}{x-4}$
$\frac{-\frac{(x-4)}{x-4} \frac{(x-4)}{x-4}}{4}$
$= \begin{cases}\frac{x-4}{x-4} & ; x \geq 4 \\ -\frac{(x-4)}{x-4} & ; x<+4\end{cases}$
$f(x)= \begin{cases}1 & ; x \geq 4 \\ -1 & ; x<4\end{cases}$
Range of f(x) is {−1, 1}
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