Let $K$ be a perfect field, $V$ an affine variety defined over $K$, $ K(V) $ and $\bar K(V)$ are the function field over $K$ and $\bar K(V)$ respectively. It says that $K(V)$ is the subset of $\bar K(V)$ fixed by $Gal(\bar K/K)$.But I don’t know how to prove it.
In the exercise, it proves $K[V]$ is the fixed subset of $\bar K[V]$ under $Gal (\bar K/K)$,so you can use this.
Thanks for any help.