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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1$\begingroup$ xkcd.com/55 $\endgroup$Brethlosze– Brethlosze2017-05-28 22:53:45 +00:00Commented May 28, 2017 at 22:53
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4$\begingroup$ This is way to broadly formulated and with way to little context. Do you mean any equation or just these two? $\endgroup$Winther– Winther2017-05-28 22:53:56 +00:00Commented May 28, 2017 at 22:53
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2$\begingroup$ Take 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 $f(f(z))=z$ $\endgroup$Winther– Winther2017-05-28 22:55:11 +00:00Commented May 28, 2017 at 22:55
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1$\begingroup$ See this wikipedia article. $\endgroup$Arthur– Arthur2017-05-28 23:09:21 +00:00Commented May 28, 2017 at 23:09
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1$\begingroup$ Assume $f(x)=ax+b$ for the second one. $\endgroup$Simply Beautiful Art– Simply Beautiful Art2017-05-28 23:11:04 +00:00Commented May 28, 2017 at 23:11
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