Is this map bijective? Is there an inverse?

Question

Is this map bijective? Is there an inverse? $f: \Bbb N_0 \rightarrow \Bbb Z$, $n \mapsto \begin{cases} n/2, & \text{if $n$ is even} \\ -{(n+1)}/{2}, & \text{if $n$ is odd} \end{cases}$

If so, how do I show this?

Thanks

Answer 1

If it is bijective it must be both injective and surjective.

Injective (1-1). For every y in the co-domain, there is at most 1 x in the domain that maps to it.

Surjective -- For every y in the co-domain, there is at least 1 x in the domain that maps to it.

If a function is bijective, then there is an inverse.