Intermediate Algebra (6th Edition)

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

Chapter 6 - Review: 4

Answer

The domain is all real numbers except $4$. $x\ne4$

Work Step by Step

We need to find the value of $x$ that would create a zero in the denominator. We do this by setting the denominator to zero and solving, $3x-12=0$ Add $12$ to both sides $3x=12$ Divide by 3 $x=4$ When $x=4$ in this function, there is a zero in the denominator. $h(4)=\frac{4(4)}{3(4)-12}=\frac{16}{0}$ Therefore the domain can be any number (all real numbers) EXCEPT $4$.
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