Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - Review Exercises: Chapter 7 - Page 496: 21


Domain = $\mathbb{R}\backslash\{-1,-4\}$ or $\{t\in \mathbb{R}\ \ |\ t\neq-1, t\neq-4\}$

Work Step by Step

The domain of a real function ( a function defined on real numbers) is the set of numbers for which f(x) is defined (for which f(x) can be calculated). Factoring the denominator, we search for factors of 4 that add to 5, ... they are 1 and 4. $f(t)=\displaystyle \frac{1}{(t+1)(t+4)}$ can be calculated for any real $t$, except $t=-1$ and $t=-4$, which yield zero in the denominator. Domain = $\mathbb{R}\backslash\{-1,-4\}$ or $\{t\in \mathbb{R}\ \ |\ t\neq-1, t\neq-4\}$
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