Let a < b < c. Suppose that f is continuous on [a, b], that g is continuous on [b, c], and that f (b) = g(b). Define h on [a, c] by h(x) := f(x) for x ∈ |a, b and h(x) := g(x) for x ∈ |b, c. Prove that h is continuous on [a, c].