Consider the function h where $h(x,y) = (x+y,x-y)$, $h : \mathbb N\times \mathbb N\to \mathbb N\times\mathbb N$
Let $g : \Bbb N \times \Bbb N \to\Bbb N \times \Bbb N$ defined as $g(m,n) = (m + n,m - n)$