1. Replace f(x) with y .
[tex]y=\sqrt[3]{x+7}[/tex]2. Replace every x with a y and replace every y with an x:
[tex]x=\sqrt[3]{y+7}[/tex]3. Solve for y:
[tex]\begin{gathered} x^3=(\sqrt[3]{y+7})^3 \\ x^3=y+7 \\ y=x^3-7 \end{gathered}[/tex]4. Replace y with f−1(x)
[tex]f^{-1}(x)=x^3-7[/tex]