Question

Find f^-1(x)

Answer 1

\[f(x) = \sqrt[3]{x - 8}\]

Answer 2

The idea is this


Step 1) Replace f(x) with y


Step 2) Swap x and y


Step 3) Solve for y to get the inverse function


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\[\large f(x) = \sqrt[3]{x - 8}\]


\[\large y = \sqrt[3]{x - 8}\]


\[\large x = \sqrt[3]{y - 8}\]


\[\large x^3 = y - 8\]


\[\large x^3+8 = y\]


\[\large y = x^3+8\]


\[\large f^{-1}(x) = x^3+8\]