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

 

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