In order to find the inverse function, let' switch x by f^-1(x) and f(x) by x in the function, then we solve for f^-1(x):
[tex]\begin{gathered} x=\sqrt[3]{f^{-1}(x)+11} \\ x^3=f^{-1}(x)+11 \\ f^{-1}(x)=x^3-11 \end{gathered}[/tex]
Therefore the correct option is D.
