Let $f$ be an entire function such that $f(z) = f(1/z)$ for all $z \in \mathbb{C} \setminus \{0\}$. Show that $f(z)$ is constant. Let $f$ be an entire function such that $f(z) = f(1/z)$ for all $z \in \mathbb{C} \setminus \{0\}$. Show that $f(z)$ is constant.
I understand Liouville's Theorem could come into play here but unsure where to apply. 

Hint: $\lim_{z\to\infty} f(z)=\lim_{z\to\infty} f(\frac{1}{z})=f(0)$. 
