Chapter 6 Rational Exponents and Radical Functions - 6.4 Use Inverse Functions - 6.4 Exercises - Skill Practice - Page 443: 20

See below

We need to show that $f(g(x))=x=g(f(x))$ $f(g(x))=f((4x)^{1/3})=\frac{1}{4}((\frac{x+2}{5})^{1/2})=5(\frac{x+2}{5})^{1/2})^{2}-2=5(\frac{x+2}{5})-2=x+2-2=x$ $g(f(x))=g(5x^2-2)=(\frac{5x^2-2+2}{5})^{1/2}=(\frac{5x^2}{5})^{1/2}=(x^2)^{1/2}=x^{2\times\frac{1}{2}}=x^1=x$ Thus we proved what we had to.