Functions

Given that for any $n \in \mathbf{N}$ there exist an odd integer $q$ and a non-negative integer $r$ such that, $n$ can be written uniquely as $n=q \times 2^r$.

Let $f: \mathbf{N} \rightarrow \mathbf{N} \times \mathbf{N}$ be function defined by $f(n)=\left(r+1, \frac{q+1}{2}\right)$. Then,