well-defined functions I am asked to argue whether or not the following two functions are well-defined (textbook definition: a) define $y$ for all $x$ in domain, and b) any is mapped to exactly one y). Both of the below functions are functions from $\mathbb{Q}$ to $\mathbb{Q}$.
$$f\left(\frac{p}{q}\right) = \frac{p+1}{q}$$
$$g\left(\frac{p}{q}\right) = \frac{p+q}{p-q}$$
My argument is that since $0$ is a rational number, we can take, for $f$, $p=0$ and $q=x$ and the function will not be defined. Similarly, we can take $p=q=0$ for $g$, and the function, again, will not be defined.
But the argument seems to be too easy. Is there something I am missing that won't allow me to use these two counter examples?
Thanks!

Your argument does not quite work because $\frac{0}{0}$ is not a rational number.  What you want to look for is two different representations of the same fraction that give different answers.  For instance
$$
f\left(\frac{1}{2}\right)=\frac{2}{2}=1,
$$
but,
$$
f\left(\frac{2}{4}\right)=\frac{3}{4}.
$$
The problem is that in $\mathbb{Q}$, $\frac{1}{2}=\frac{2}{4}$, but the function is not the same for both.
