Question

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

• A. $[0,3]$
• B. $[3,6]$
• C. $[0,6]$
• D. $[0,2]$

Answer 1

The correct option is B $[3,6]$

$f\left(x\right)=2|x-1|+|x+2|$

$f\left(x\right)=\{\begin{array}{cc}-2(x-1)+x+2,& -1\le x<1\\ 2(x-1)+x+2,& 1\le x\le 2\end{array}$

$=\{\begin{array}{cc}4-x,& -1\le x<1\\ 3x,& 1\le x\le 2\end{array}$