What is the range of the function
Question:

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

Solution:

$f(x)=\frac{|x-1|}{x-1}=\frac{\pm(x-1)}{x-1}=\pm 1$

Range of $f=\{-1,1\}$