Prove of continuity and open set

I need to prove this but I can’t figure out how. It would be nice if somebody can help me out with this .

Let X and Y be nonempty subsets of $R^{N}$ and $R^{K}$, respectively. Prove the followings:

A function $f: X rightarrow Y$ is continuous if and only if for any open set $B subset Y $, the inverse image of $B$ under $f$,

$f^{-1} = {x in X | f(x) in B }$
is open.