Answer to Question #259567 in Algebra for Mae

Question

Find the inverse function of g(x)=(x+2)³

Answer 1

$g(x)=(x+2)^3\\let\space y=g(x)=(x+y)^3\\y=(x+2)^3\\y^{\frac{1}{3}}=x+2\\x=y^{\frac{1}{3}}-2\\x=\sqrt[3]{y}-2\\g^{-1}(y)=x\\g^{-1}(y)=\sqrt[3]{y}-2\\g^{-1}(x)=\sqrt[3]{x}-2\\$

inverse=$\sqrt[3]{x}-2$