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 \(\x\).