Problem

For the function $f(x)=(x-9)^{\frac{1}{3}}$, find $f^{-1}(x)$.

Answer

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Answer

\(\boxed{f^{-1}(x) = x^3 + 9}\)

Steps

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 ：\(\boxed{f^{-1}(x) = x^3 + 9}\)

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