Let $K$ be an extencion of $F$ and let $a,b\in K$. If $a$ is not algebraic in $F$, but it is in $F(b)$, show that $b$ is algebraic in $F(a)$

Question

Let $K$ be an extencion of $F$ and let $a,b\in K$. If $a$ is not algebraic in $F$, but it is in $F(b)$, show that $b$ is algebraic in $F(a)$.

$F(x)$ is the smaller subfield of $K$ containing $F$ and $x$.

I'm not used to problem abouth field extentions and algebraic numbers, I just know the definition, so I need some help with this problem. Thanks.