Show that f(x,y)=x+y (with |x|=|y|) isn't a one way function

Question

I have to prove that the function $f\colon \mathbb N × \mathbb N \to \mathbb N$ defined by $f(x, y) = x + y$ and $|x| = |y|$ isn't a one-way function. How do I go around doing that?

Answer 1

A function $f$ is one-way if given $f(z)$ for random $z$, it is hard to find an input $w$ such that $f(w) = f(z)$. So in order to show that $f$ isn't one way, you need to show that given $f(z)$ for random $z$, it is not hard to find an input $w$ such that $f(w) = f(z)$. Good luck!