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

To check if the function is one-one:If $n$ is odd, let $n=2k-1$. Then $f(2k-1)=\frac{2k-1-1}{2}=k-1$. For $k=1,2,3\dots$, the values are $0,1,2,\dots$.If $n$ is even, let $n=2k$. Then $f(2k)=-\frac{2k}{2}=-k$. For $k=1,2,3\dots$, the values are $-1,-2,-3,\dots$.Since the set of values for odd $n$ ($\{0,1,2,\dots \}$) and even $n$ ($\{-1,-2,-3,\dots \}$) are disjoint and cover all integers, every integer is mapped to exactly one natural number.Therefore, the function is both one-one and onto (bijective).