How should i solve expressions in $f$?
$$ f(f(x))=e^x $$
or:
$$ f(f(x+1)+1)=x $$
Series, expansions, discretizations, CAS, whatever?
My normal approach is useless here...
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What is your normal approach? – projectilemotion May 28 '17 at 22:52
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1https://xkcd.com/55/ – Brethlosze May 28 '17 at 22:53
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4This is way to broadly formulated and with way to little context. Do you mean any equation or just these two? – Winther May 28 '17 at 22:53
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I mean, those look always as simple expressions, but most of them dont show a simple solution at all..... – Brethlosze May 28 '17 at 22:54
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2Take a look at these related questions: thoughts about $f(f(x))=e^x$ ; How to calculate $f(x)$ in $f(f(x))=e^x$? ; Find all continuous functions $f:\mathbb R\to\mathbb R$ such that $f(f(x))=e^{x}$ ; Find all entire $f$ such that $f(f(z))=z$ – Winther May 28 '17 at 22:55
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the second $f(f(x+1)+1)=x$ is $f(x)=x-1$ – Jacob Claassen May 28 '17 at 22:57
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I never though that would be so difficult and complex....... – Brethlosze May 28 '17 at 22:59
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1See this wikipedia article. – Arthur May 28 '17 at 23:09
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1Assume $f(x)=ax+b$ for the second one. – Simply Beautiful Art May 28 '17 at 23:11
