$ f\circ f\circ f(x) = f(3x) $
Ignoring trivial (constant) solutions, I am not sure what I can try as an initial guess.
Also, how does this generalise?
i.e. If $f^k(x) = f \circ f \circ f\circ ...(x)$ composed $k$ times, then what are the generalised solutions? (if any)