Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.1 - Functions - Exercises: 72


The domain of this function is $(-3,3)$

Work Step by Step

$f(x)=\dfrac{x}{\sqrt[4]{9-x^{2}}}$ This function is undefined for negative values of the expression inside the square root and also for the values of $x$ that make the denominator equal to $0$. Its domain can then be found by solving the following inequality: $9-x^{2}\gt0$ Find the intervals. Factor the left side of the inequality: $(3-x)(3+x)\gt0$ The factors are $3-x$ and $3+x$. Set them equal to $0$ and solve for $x$: $3-x=0$ $x=3$ $3+x=0$ $x=-3$ The factors are $0$ when $x=3,-3$. These numbers divide the real into the following intervals: $(-\infty,-3)$ $,$ $(-3,3)$ $,$ $(3,\infty)$ Elaborate a diagram, using test points to determine the sign of each factor in each interval: (refer to the attached image below) It can be seen from the diagram that only the interval $(-3,3)$ satisfies the inequality. Also, since it involves the sign $\gt$, the endpoints of this interval do not satisfy the inequality. The domain of this function is $(-3,3)$
Small 1501097165
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.