Question

Find the range of the following function :

$f\left(x\right)=\frac{|x-4|}{x-4}$

• A. $[-1,1]$
• B. $[-\frac{\pi }{2},\frac{3\pi }{2}]$
• C. $(-2\pi ,0]$
• D. $[\frac{-3\pi }{2},\frac{\pi }{2}]$

Answer 1

The correct option is A $[-1,1]$

We have, $f\left(x\right)=\frac{|x-4|}{x-4}$

Clearly, $f\left(x\right)$ is defined for all $x\in R$ except at $x=4$. Therefore, Domain $\left(f\right)=R-\left\{4\right\}$

Now,

$f\left(x\right)=\frac{|x-4|}{x-4}$

$f\left(x\right)=\frac{x-4}{x-4}=1,ifx>4$

$f\left(x\right)=\frac{-(x-4)}{x-4}=-1,ifx<4$

Hence, Range $\left(f\right)=\{-1,1\}$