Question

The range of the function $f\left(x\right)=\frac{\left|x-4\right|}{x-4}$ is __________ .

Answer 1

$$\begin{gathered} f\left(x\right)=\frac{\left|x-4\right|}{x-4}\frac{-{\displaystyle \frac{\left(x-4\right)}{x-4}}{\displaystyle \frac{\left(x-4\right)}{x-4}}}{4} \\ =\left\{\begin{array}{l}\frac{x-4}{x-4};x\ge 4\\ -\frac{\left(x-4\right)}{x-4};x<+4\end{array}\right. \\ f\left(x\right)=\left\{\begin{array}{l}1;x\ge 4\\ -1;x<4\end{array}\right. \end{gathered}$$
Range of f(x) is {−1, 1}