Find inverse functions for simple invertible functions, including rational examples.
Find an inverse function by swapping x and y and solving a square root equation
Problem
Find \(f^{-1}(x)\) and its domain for \(f(x)~=~\sqrt{x~-~4}~+~2\).
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What this problem is really about
Before inverting a square-root rule, record its domain and range so their exchange is not lost in the algebra. Swap input and output, isolate the radical, and square only after recognizing the nonnegative side supplied by the inverse domain. Finish by attaching the original range as the inverse domain and checking that the reversed operations make sense.
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