Answer
${f}^{-1}$(${x}$)= $\sqrt[3] {x}$-2
Work Step by Step
${y}$=${(x+2)}^{3}$
Switch x and y then solve for y to find inverse:
${x}$=${(y+2)}^{3}$
${\sqrt[3] {x}}$=${y+2}$
${\sqrt[3] {x}}$-2=${y}$
${f}^{-1}$($f({x})$)=x
${f}^{-1}$($f({x})$)=$\sqrt[3] {(x+2)^{3}}$-2
${f}^{-1}$($f({x})$)=${x}$+2-2
${f}^{-1}$($f({x})$)=x
