Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 7 - Rational Functions - 7.1 Rational Functions and Variation - 7.1 Exercises - Page 566: 49


The domain of this function is all real numbers.

Work Step by Step

To find the domain of this function, we need to find which values are excluded for $a$. In a rational function, the denominator cannot equal $0$ because the function would be undefined. Therefore, we need to set the denominator equal to $0$ and solve for $a$: $a^2 + 9 = 0$ Subtract $9$ from each side of the equation: $a^2 = -9$ If we take the square root of both sides, we will end up with a non-real number. Therefore, there are no restrictions on $x$, and the domain of this function is all real numbers.
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