Find inverse functions for simple invertible functions, including rational examples.
Find an inverse function by swapping x and y and solving a rational equation
Problem
Find \(f^{-1}(x)\) and its domain exclusion for \(f(x)~=~1/(x~-~2)~+~3\).
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What this problem is really about
For a shifted reciprocal, swap input and output first, then isolate the reciprocal expression before taking reciprocals. Reversing too early would apply the operation to a sum instead of the isolated fraction. Once the new output is solved, its denominator exclusion should agree with the output value the original reciprocal could never attain.
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