SOLUTION
To find the inverse, first, we will make x the subject of the formula:
[tex]\begin{gathered} y=\sqrt[3]{x-9} \\ \text{Cube both sides} \end{gathered}[/tex][tex]\begin{gathered} y^3=(\sqrt[3]{x-9})^3 \\ y^3=x-9 \\ y^3+9=x \end{gathered}[/tex]Now we will replace x with f-inverse and replace y with x in the above expression:
[tex]\begin{gathered} f^{-1}(x)=x^3+9 \\ \text{The correct answer is D.} \end{gathered}[/tex]
