Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.2 Representing Functions - 1.2 Exercises - Page 21: 3


The domain of the rational function $$f(x)=\frac{P(x)}{Q(x)}$$ is $$\mathcal{D}=\{x|x\in\mathbb{R},Q(x)\neq0\}.$$

Work Step by Step

Let $$f(x)=\frac{P(x)}{Q(x)}$$ where $P$ and $Q$ are polynomials. The rational function is defined at every real $x$ that satisfies $Q(x)\neq0$. In other words we have to throw away all the real zeros of the polynomial function $Q(x)$: $$\mathcal{D}=\{x|x\in\mathbb{R},Q(x)\neq0\}=\mathbb{R}/\{x|Q(x)=0\}.$$
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