Intermediate Algebra (6th Edition)

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

Chapter 6 - Review: 6

Answer

The domain is all real numbers, except $4$ and $-4$.

Work Step by Step

To find the values of $x$ that create a zero in the denominator, set the denominator equal to zero and solve. $3x^{2}-48=0$ Factor $3(x^{2}-16)=0$ Using the Zero Product Property $3=0$ and $x^{2}-16=0$ The first equation is false. The second equation $x^{2}-16=0$ Add $16$ to both sides $x^{2}=16$ Square root both sides $x=4$ and $x=-4$ Therefore, the two values that $x$ cannot be are $4$ and $-4$. The domain is all real numbers EXCEPT these two values.
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