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: 69

Answer

Domain: $(4,\ \infty)$

Work Step by Step

We are given: $f(x)= \frac{3}{\sqrt{x-4}}$ The domain of a function consists of all the values that $x$ is allowed to have. In this case, we can not take the square root of a negative number: $x-4\ge 0$ $x\ge 4$ In addition, we can not have division by $0$: $x-4\ne 0$ $x\ne 4$ Thus overall: $x\gt 4$. Therefore, the domain is: $(4,\ \infty)$
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