Question

Write F(x)= lxl-2 as a piecwise function

Answer 1

By definition, you have

$|x| = \begin{cases} x \text{ if } x\geq 0\\ -x\text{ if } x<0\end{cases}$

So, in your case, you have

$|x|-2 = \begin{cases} x-2 \text{ if } x\geq 0\\ -x-2 \text{ if } x<0\end{cases}$