# The range of the function f(x)

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}