Even extension

Find the even extension of $$f(x)=\begin{align}\begin{cases}x^2-x^3,&\quad 0\leq x<3\\4-x,&\quad x\geq 3.\end{cases}\end{align}$$

---

We know $|x|$ is an even function. We thus have $$g(x)=\begin{align}\begin{cases}|x|^2-|x|^3,&\quad 0\leq |x|<3\\4-|x|,&\quad |x|\geq 3,\end{cases}\end{align}$$ or $$g(x)=\begin{align}\begin{cases}x^2+x^3,&\quad -3<x\leq 0\\4-|x|,&\quad x>3 \vee x<-3\\x^2-x^3,&\quad 0\leq x<3.\end{cases}\end{align}$$