Chapter 6 Rational Exponents and Radical Functions - 6.4 Use Inverse Functions - 6.4 Exercises - Skill Practice - Page 443: 17

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We need to show that $f(g(x))=x=g(f(x))$ $f(g(x))=f((4x)^{1/3})=\frac{1}{4}((4x)^{1/3})=\frac{1}{4}(4x)^{\frac{1}{3}\times3}=\frac{1}{4}4x=x$ $g(f(x))=g(\frac{1}{4}x^3)=(4(\frac{1}{4}x^3))^{1/3}=(x^3)^{1/3}=x^{3\times\frac{1}{3}}=x^1=x$ Thus we proved what we had to.