I really need help concerning this task: let $f : X \to \mathbb{R}^n$, $X\subseteq \mathbb{R}^n$, be a function with $X$ open.
Show: $f$ is continuous $\iff f^{-1} (W) $ is open for every open $W \subseteq\mathbb{R}^n$, when $f^{-1}$ is the inverse of $f$.
Thanks for your help.