College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Chapter P Review - Exercises - Page 77: 95


$\displaystyle\{x|x\geq 0$ and $x\neq 4\}$

Work Step by Step

We know that $\displaystyle \frac{\sqrt{x}}{x^{2}-3x-4}$ is undefined whenever the denominator is 0, so: $x^2-3x-4=(x+1)(x-4)=0$ $x=-1, x=4$ The equation is also undefined when taking the square root of a negative number ($x\lt0$). Combining these restrictions, we get the domain: $\{x|x\geq 0$ and $x\neq 4\}$
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