Question

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

• A. $[6,8]$
• B. $[2,4]$
• C. $[0,4]$
• D. $\{1,2\}$
  
  

Answer 1

The correct option is A $[6,8]$

$f\left(x\right)=|x-1|+|x-2|+|x+1|+|x+2|$
when $xϵ[-2,-1]$
$f\left(x\right)=-(x-1)-(x-2)-(x+1)+(x+2)=-2x+4$
when $xϵ[-1,1]$, $f\left(x\right)=-(x-1)-(x-2)+x+1+x+2$
$=-x+1-x+2+x+1+x+2=6$
when $xϵ[1,2]$, $f\left(x\right)=(x-1)-(x-2)+x+1+x+2=2x+4$
Plotting the graph of the function, range of $f\left(x\right)=[6,8]$