I need some support in order to make the graph of $f(x)$ where $f(f(x))=e^x$. I'm also interested in the limits of $f(x)$ at +/-$\infty$. This function has really aroused my curiosity and I'd like to find out more information on it.
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Are there any conditions on $f$ such as continuity or even differentiability? – Stefan Geschke Aug 08 '12 at 11:19
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1See a more general question of this nature here: http://mathoverflow.net/questions/17614/solving-ffxgx and further links from there. And also here: http://math.stackexchange.com/questions/3633/square-root-of-a-function-in-the-sense-of-composition – Harald Hanche-Olsen Aug 08 '12 at 11:27
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@ Stefan Geschke: I didn't take into account any specific condition. – user 1591719 Aug 08 '12 at 11:34
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3exactly yours question http://mathoverflow.net/questions/12081/does-the-exponential-function-have-a-square-root – Norbert Aug 08 '12 at 11:38
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This is related. – J. M. ain't a mathematician Aug 08 '12 at 13:24
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Take a look at the "tetration" web pages, use Google. (I try to avoid a re-hash of that material here...) – GEdgar Aug 08 '12 at 14:22
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This realm of mathematics seems to be surrounded by much mystery. – user 1591719 Aug 08 '12 at 14:35