Question

Redefine the function $f\left(x\right)=\left|x-2\right|+\left|2+x\right|,-3\le x\le 3$

Answer 1

$f\left(x\right)=|x-2|+|2+x|-3\le x\le 3$

Redefining function in $-3\le x\le 3$

$f\left(x\right)=\{\begin{array}{c}2-x-2-x\\ 2-x+2+x\\ x-2+2+x\end{array}\begin{array}{cc}=-2x;& -3\le x\le -2\\ =4;& -2\le x\le 2\\ =2x;& 2\le x\le 3\end{array}$