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