If $f:N\to W$ defined by $f\left(n\right)=\left\{\begin{array}{l}\frac{n}{2} when n is even\\ 0 when n is odd\end{array}\right.$  then the funciton $f$ is 

The given function is $f\left(x\right)=\left\{\begin{array}{l}\frac{x}{2} when x is even\\ 0 when x is odd\end{array}\right.$

The domain is set of all natural numbers and codomain is set of whole numbers.

For every odd number, image is same, for example $f\left(3\right)=f\left(5\right)=0$, so it is not one one

For every number $y\in N$, there exists even number such that $y=2x\in N$

Therefore, the function is not one one but onto