Let $F$ ba an extension extension of the field $K$. An element $a$ in $F$ is said to be algebraic if $a$ is the root of some non-zero polynomial $f \in K[x]$.
Using only the definition, how do we prove that for a field of rational functions, $K(x_1, x_2, ... x_n)$, over a field $K$,
(a) $x_i$ is transcendental over K
(b) Every non-constant rational function is transcendental over K