Here is a problem I made up:
Find all differentiable functions $f$ from the reals to the reals such that $f(f(x))=f'(x)$ for all real $x$.
Asked
Active
Viewed 116 times
1
-
It can't be $f(x)=A_{1}x^{a_1}+A_{2}x^{a_2}+\cdots +A_nx^{a_n}$ for any real $A_i,a_i$ (wlog $\max{a_i}=a_1$), since $a_1^2=a_1-1$ is impossible. – user26486 Apr 18 '15 at 18:52
-
if we assume that $f(0)=0$ then $f=0$ see this question – Elaqqad Apr 18 '15 at 18:54
-
2see also this – Blex Apr 18 '15 at 18:54