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