I am stuck trying to solve the following functional equation for $h: \mathbb{R} \rightarrow \mathbb{R}$:
$\tanh{(h(c(g))} = \tanh^2{(h(g))}$,
where $c(g) = \frac{1}{4}\left(2+7g - (5g+2)\cos(\pi g)\right)$.
I have tried expanding $h$, $\tanh$ and $c$ as power series then solving for the coefficients of $h$ recursively but that did not work. I'm not sure if $h$ can be expressed in terms of elementary functions either.
Thanks for any help