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!

You might want to think of the question like this, with $r =\frac pq$
For the first case $f(r) = r + \frac 1q$
For the second case note that $q\neq 0 $ if $r$ is rational, and $f(r) = \frac {r+1}{r-1}$
A well-defined function is one for which you can determine a single defined value for each $r$.
