Find as many different pairs of functions, \(f\) and \(g\), as possible such that:

\(f(g(x)) = g(f(x)) \)

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Here are some examples but there are infinitely many more:

\( f(x) = x + 5, \; g(x) = x + 7 \)

\( f(x) = 5x, \; g(x) = 7x \)

\( f(x) = x^2, \; g(x) = \sqrt{x} \)

\( f(x) = e^x, \; g(x) = \ln x \)

For a more general solution see this paper

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