Let $f\colon U\to U$ be a homeomorphism, where $U\subset \mathbb R$ is an open set. By the definition, a fixed point $p\in U$ is attracting if there exists $e > 0$ s.t. if $|x-p| < e$ for some $x\in U$, then $f^n(x)$ tends to $p$. And a fixed point $p$ is repelling if for every $e > 0$ and for every $x$ condition $|x-p| < e$ implies existence of some $k$ such that $|f^k(x)-p| > e$.
My professor stated that $p$ being attracting fixed point for $f^{-1}$ is equivalent to $p$ being repelling for $f$. How can this be proven?