abstract algebra – Show that element \$a\$ is algebraic over \$F\$ if \$f(a)\$ is algebraic over \$F\$.

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…