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Results tagged with functional-equations
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user 25619
8
votes
Existence of function satisfying $f(f'(x))=x$ almost everywhere
Looking for a solution of the form $f(x)=ax^b$, $x>0$, one finds
$$
a = \phi^{-\phi/(\phi+1)}, ~~~ b=\phi
$$
where $\phi=\frac{\sqrt{5}+1}{2}$ is the Golden ratio.
- 664