Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Review: 5

Answer

The domain is all real numbers except $0$ and $-8$.

Work Step by Step

To find the values of $x$ at which the denominator equals zero, set the denominator equal to zero and solve. $x^{2}+8x=0$ Factor: $x(x+8)=0$ Using the Zero Product Property $x=0$ and $x+8=0$ The first equation is already solved: $x=0$ The second equation: $x+8=0$ Subtract $8$ from both sides $x=-8$ These two values of $x$, $0$ and $-8$, create an undefined fraction within the function. Therefore, the domain is all real numbers EXCEPT $0$ and $-8$.
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