Theorem: Suppose $f: \real^d \to \real^k$, $g: \real^k \to \real$, and $h: \real^d \to \real$ is the composition of $f$ and $g$ defined by

\[h(\x) = g(f(\x)).\]

If $f$ is continuous at a point $\x \in \real^d$ and if $g$ is continuous at the point $f(\x)$, then $h$ is continuous at $\x$.