How to find a continuous function $f(x)$ for $x > 12$, such that $f(f(x))=\ln(x)$? Preferably analytic too.
A function $f(x)$ such that $f(f(x))=\ln(x)$
3
$\begingroup$
real-analysis
functional-equations
-
0Since x>\exp(\dots\exp(1)\dots) with $n-1$ exponents, we get $f_n\le (\ln(\ln x))^a$. Sorry, no more time now. – 2012-01-09