Let `f : N->N`be defined by `f(n)={((n+1)/2,"if n is odd " ), (n/2,"if n is even "):}`for all `n in N`. State whether the function f is bijective. Justify your answer.

Explanation

To determine whether the function \( f : \mathbb{N} \to \mathbb{N} \) 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}
...