Problem
For the function $f(x)=(x-9)^{\frac{1}{3}}$, find $f^{-1}(x)$.
Solution
Step 1 ：\(f(x) = (x-9)^{\frac{1}{3}}\)
Step 2 ：\(x = (f^{-1}(x)-9)^{\frac{1}{3}}\)
Step 3 ：\(x^3 = f^{-1}(x)-9\)
Step 4 ：\(f^{-1}(x) = x^3 + 9\)
Step 5 ：\(\boxed{f^{-1}(x) = x^3 + 9}\)
