1. The problem asks which of the functions \(g(x) = \sqrt[5]{x}\) and \(h(x) = \sqrt[3]{x}\) are continuous for all real numbers. 2. Recall that the \(n\)-th root function \(f(x) = \sqrt[n]{x} = x^{\frac{1}{n}}\) is continuous for all real numbers if \(n\) is an odd integer because odd roots of negative numbers are defined in the real numbers. 3. For \(g(x) = \sqrt[5]{x} = x^{\frac{1}{5}}\), since 5 is an odd integer, \(g(x)\) is continuous for all real numbers. 4. For \(h(x) = \sqrt[3]{x} = x^{\frac{1}{3}}\), since 3 is also an odd integer, \(h(x)\) is continuous for all real numbers. 5. Therefore, both \(g\) and \(h\) are continuous for all real numbers. Final answer: C Both \(g\) and \(h\)