Find inverse functions for simple invertible functions, including rational examples.
Find the inverse of a cube-root function by swapping x and y and solving
Problem
Find \(f^{-1}(x)\) for \(f(x)~=~\sqrt[3]{x~-~3}~+~5\).
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What this problem is really about
Cube-root functions are one-to-one across all real inputs, so their inverses need no branch decision. After swapping input and output, isolate the cube root and undo it by cubing the entire grouped expression. Keeping that group intact matters: cubing a binomial is not the same as cubing its terms separately.
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