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.
The graph of $f(x)$ where $f(f(x))=e^x$
10
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calculus
real-analysis
limits
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0Are there any conditions on $f$ such as continuity or even differentiability? – 2012-08-08
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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 – 2012-08-08
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0@ Stefan Geschke: I didn't take into account any specific condition. – 2012-08-08
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3exactly yours question http://mathoverflow.net/questions/12081/does-the-exponential-function-have-a-square-root – 2012-08-08
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0[This](http://math.stackexchange.com/questions/59023) is related. – 2012-08-08
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0Take 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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0This realm of mathematics seems to be surrounded by much mystery. – 2012-08-08