Hello !
I have a problem to solve this question :
Find all real continuous functions f verifing : f(x+1)=f(x)+f(1/x)
Have you ever seen this, could you help me please ?
Yes we can already proove that :
$\displaystyle f(0)=f(\Phi^{-1})=f(-\Phi)=0$ where $\displaystyle \Phi$ is the Gold number : $\displaystyle \frac{1+\sqrt 5}{2}$
and
$\displaystyle f$ has a limit when $\displaystyle x\rightarrow\infty$, $\displaystyle f\rightarrow f(1)$