Let $L=\mathbb{C}(t)$ (where $t$ is an indeterminate). Let $\phi\colon L\to L$ be the $\mathbb{C}$-automorphism of $L$ given by $\phi(t) = \frac{3t-2}{4t-3},$ and let $G$ be the group generated by $\phi$. Find the fixed field of $G$.
Could really use some help with this. Thanks!