Find inverse functions for simple invertible functions, including rational examples.
Find the inverse of a logarithmic function by swapping x and y
Problem
Find \(f^{-1}(x)\) for \(f(x)~=~\log_{2}(x)\).
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What this problem is really about
A logarithm reports the exponent placed on its base, so its inverse should reverse that question. After swapping the variables, convert the logarithmic statement to equivalent exponential form without changing the base. The original logarithm’s domain and range then exchange roles, providing a built-in check on the inverse’s input and output sets.
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