This question is from the book Abstract Algebra: Theory and Applications by Thomas W. Judson.
Chapter 1 – Question 17
Which of the following relations $f : \mathbb{Q} \to \mathbb{Q}$ define a mapping? In each case, supply a reason why $f$ is or is not a mapping.
(a) $f\left(\frac{p}{q}\right) = \frac{p + 1}{p – 2}$
(b) $f\left(\frac{p}{q}\right) = \frac{3p}{3q}$
(c) $f\left(\frac{p}{q}\right) = \frac{p + q}{q^2}$
(d) $f\left(\frac{p}{q}\right) = \frac{3p^2}{2} – \frac{7q^2}{2} – \frac{p}{q}$