College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.1 - Functions - 2.1 Exercises: 58

Answer

$(-\infty,\ -3)\cup (-3,2)\cup (2,\ \infty)$

Work Step by Step

We are given: $f(x)= \frac{x^{4}}{x^{2}+x-6}$ The domain of a function consists of all values that $x$ is allowed to have. In this case, we can not have division by $0$: $x^{2}+x-6\neq 0$ $(x+3)(x-2)\neq 0$ $(x+3)\neq 0$ or $(x-2)\neq 0$ $ x\neq-3$ or $x\neq 2$ Thus the domain is: $(-\infty,\ -3)\cup (-3,2)\cup (2,\ \infty)$
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