if $f$ and $g$ are continuous, then $g \circ f$ is continuous

how can we prove that by using this definition of continuous:

$f : \mathbb{R} \to \mathbb{R}$ is said to be continuous if for each open subset $V$ of $\mathbb{R}$ , $f^{-1}(V)$ is an open subset of $\mathbb{R}$

please,help me with that how can I do it?