Exercise 9

Let \(f : \mathbb{N} \to \mathbb{N}\) be defined by
\[ f(n) = \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] for all \(n \in \mathbb{N}\).
State whether the function \(f\) is bijective. Justify your answer.