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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?2012-08-08
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    See 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-composition2012-08-08
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    @ Stefan Geschke: I didn't take into account any specific condition.2012-08-08
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    exactly yours question http://mathoverflow.net/questions/12081/does-the-exponential-function-have-a-square-root2012-08-08
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    [This](http://math.stackexchange.com/questions/59023) is related.2012-08-08
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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...)2012-08-08
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    This realm of mathematics seems to be surrounded by much mystery.2012-08-08

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