Really basic parametric equations question

Hi, this is really simple but I just wanted to make sure that since it is so simple that I am not missing something,

Consider the parametric equations

$\displaystyle x=f(\xi)$

and $\displaystyle y=g(\xi)$

where x is of degree $\displaystyle N$and y of degree $\displaystyle n$

then since math $\displaystyle \xi=f^{-1}(x)$ which I believ would have degree $\displaystyle \frac{1}{N}$

and to get our equation into regular form with y as a dependent and x an independent variable we must take

$\displaystyle y=g(f^{-1}(x))$

will our final function in terms of x and y be of degree $\displaystyle \frac{n}{N}$?