Problem $2$: Functions

Let $Z=\{dots-2,-1,0,1,2,$dots$\}$ denote the set of integers. Suppose $f$:$ZZ$ is a function

defined by: $f(n)=\frac{n}{2}$ if $n$ is even, and $n-1$ if $n$ is odd

Prove or disprove each of the following:

$($a$)f$ is one$-$to$-$one $($injective$)$

$($b$)f$ is onto $($surjective$)$