Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 229: 83

$(f~o~g)^{-1}=2\sqrt[3] {(x+3)}$

$f~o~g=f(g(x))=f(x^3)=\frac{1}{8}x^3-3~~$ (Replace $f~o~g$ by $y$): $y=\frac{1}{8}x^3-3~~$ (Interchange $x$ and $y$): $x=\frac{1}{8}y^3-3$ $x+3=\frac{1}{8}y^3$ $y^3=8(x+3)$ $y=\sqrt[3] {8(x+3)}$ $y=2\sqrt[3] {(x+3)}$ $(f~o~g)^{-1}=2\sqrt[3] {(x+3)}$