Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 7 - Functions - Exercise Set 7.1 - Page 395: 34

Answer

Student D is correct, as multiplying $m, n$ by constants yields different values, so the function is not well-defined.

Work Step by Step

Consider the pairs of integers $m = 4, n = 3$ and $m = 8, n = 6$. From the definition, the first pair yields $\frac{16}{3}$ as the result, while the second pair yield $\frac{64}{6} = \frac{32}{3}$ as the result. As these are not equal, this means $h(\frac{m}{n})$ is not well defined.
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