Question

What is the range of the function $f\left(x\right)=\frac{\left|x-1\right|}{x-1}?$

Answer 1

$$\begin{gathered} f\left(x\right)=\frac{\left|x-1\right|}{x-1}=\frac{\pm \left(x-1\right)}{x-1}=\pm 1 \\ \text{Range of}f=\left\{-1,1\right\} \end{gathered}$$