Solutions to functional equation $f(f(x))=x$ Is there any more solutions to this functional equation $f(f(x))=x$?
I have found: $f(x)=C-x$ and $f(x)=\frac{C}{x}$.

In fact this belongs to a functional equation of the form http://eqworld.ipmnet.ru/en/solutions/fe/fe2315.pdf.
Let $\begin{cases}x=u(t)\\f=u(t+1)\end{cases}$ ,
Then $u(t+2)=u(t)$
$u(t)=\theta(t)$ , where $\theta(t)$ is an arbitrary periodic functions with period $2$
$\therefore\begin{cases}x=\theta(t)\\f=\theta(t+1)\end{cases}$ , where $\theta(t)$ is an arbitrary periodic functions with period $2$
