Consider the functions $f: \mathbb{r}^3 \rightarrow \mathbb{r}$ and $g: \mathbb{r} \rightarrow \mathbb{r}^3$ defined by \[ f(x, y,z) = \left\{ \begin{array}{ll} x+y+z & \ \text{if $xyz=0$} \\ 0 & \ \text{otherwise} \end{array} \right. \hspace{.8in} g(x) = \left\{ \begin{array}{ll} (x,2x, x^2) & \ \text{if $x\neq 0$} \\ (0,0,0) & \ \text{otherwise} \end{array} \right. \] \begin{enumerate} \item check whether $f$ and/or $g$ are injective, surjective, and/or bijective. \item find the compositions $f\circ g$ and $g\circ f$, if/when possible.