Extension field: a question about algebric extension field

Question

Def. Let $K\subseteq L$ be a field extension, and let $B$ be a subset of $L$. We denote by $K(B)$ the smallest subfield of $L$ containing both $K$ and B.

Question. Suppose that we have proved that $$L=K(B).$$ Can I conclude that $L$ is algebraic over $K(B)$?

Answer 1

I thought it is good for you to see it.

Let $K$ be field and $u\in K$, then $u$ is the root of $x-u\in K[x]$, therefore, algebraic over $K.$