I want to prove that $a$ is algebraic over $F$, if $f(a)$ is algebraic over $F$, when $E/F$ is a field extension and $a$ is in $E$. I think, I have to find $h(x)$ such that $h(x)=g(f(x))$ which is in $F(x)$. But I don’t know how to approach it…

Thank you for your help!