Question #259567

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

1
Expert's answer
2021-11-01T18:19:59-0400

g(x)=(x+2)3let y=g(x)=(x+y)3y=(x+2)3y13=x+2x=y132x=y32g1(y)=xg1(y)=y32g1(x)=x32g(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=x32\sqrt[3]{x}-2


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