Show that the functional equation $f(f(x))=-x^{3}+g(x)$ has no continuous solution.Here $g$ is a continuous periodic function with positive period.

Question

I want to show $f(f(x))=-x^{3}+g(x)$ has no continuous solution $f:\mathbb{R}\to\mathbb{R}$.Here $g$ is a continuous periodic function with its period $T>0.$ Any help will be thanked.