A function f from the set of natural numbers to integers defined by $f(n)=\left\{\begin{matrix}\frac{n-1}{2},&when\,n\,is\,odd\\-\frac{n}{2},&when\,n\,is\,even\end{matrix}\right.$ is

one-one and onto both

Clearly, range (f) = Z (Set of integers)

So, f is onto.

We observe that distinct odd natural numbers are mapped to distinct non-negative integers and distinct even natural numbers are mapped to distinct negative integers.

So, f is one-one.

Hence, f is both one-one and onto.