QuestionFind the inverse of the one-to-one function $f(x)=x^{3}-8$.

Studdy Solution
Finally, we take the cube root of both sides to solve for $y$.
$$y = \sqrt[3]{x +8}$$This is the inverse of the function $f(x)$, which we denote as $f^{-1}(x)$.
$$f^{-1}(x) = \sqrt[3]{x +8}$$The inverse of the function $f(x) = x^{3} -8$ is $f^{-1}(x) = \sqrt[3]{x +8}$.