I'm not terribly familiar with field theory, so I'd appreciate some help understanding this homework problem. For context, this problem is for an algebraic geometry course, in relation to function fields of varieties.
Let $k\subseteq L$ be a field extension. Let $S, R\subset L$ be two subsets. Show that if $k(S)$ is finite over $k$ and $k(R)$ is finite over $k$, then $k(S,R)$ is finite over $k$.
My question is: what exactly does it mean that $k(blah)$ is finite over $k$? And is this equivalent to having transcendence degree of $0$?