What is the range of the function f(x)=|x-1|/(x-1)?

Question

What is the range of the function

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

Answer 1

Given,

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

Obvisously, 

Now, 

(i) ∀x > 1, 

\(f(x)=\frac{(x-1)}{(x-1)}\) = 1,

(ii) ∀x < 1,

\(f(x)=\frac{-(x-1)}{(x-1)}\) = -1

i.e., f(x) = -1,1

∴ Range of f(x) = {-1,1}.