Question

The range of the function $f\left(x\right)=|2x+1|-2|x-1|,$ $xϵR,$ is

• A. $[-3,3]$
• B. $[0,6]$
• C. $R$
• D. none of these

Answer 1

The correct option is A $[-3,3]$

$f\left(x\right)=\mid 2x+1\mid -2\mid x-1\mid$
Now if $-\infty <x\le -1/2$
$f\left(x\right)=-(2x+1)+2(x-1)=-3$
if $-1/2<x\le 1$
$f\left(x\right)=(2x+1)+2(x-1)=4x-1$
if $1<x\le \infty$
$f\left(x\right)=(2x+1)-2(x-1)=3$
Hence Range of $f\left(x\right)$ is $[-3,3]$