If f(f(x)) = exp(x), then what is f(x)?(adsbygoogle = window.adsbygoogle || []).push({});

I don't think that f(x) can be an entire function. It would be nice to have f(x) be monotonically increasing for positive x. I tried to attack this problem by using a method in the book "Bypasses", and it works, but it involves numerical calculation of a power series and reversion of the series, and applying the two power series together, and seems very inelegant and I'm not even sure if it will converge.

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# F(f(x)) = exp(x)

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