Find all entire functions with $f(z) = f(\frac{1}{z})$, for all $z\ne 0$.

I tried to use the power series of $f$ but this did not help. I also tried to use Liouville's Theorem on $\frac{f(z)}{f(\frac{1}{z})}$ but then I have to deal with possible singularities.

Can someone help me with this problem?