Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.1 Properties of Functions - 2.1 Exercises - Page 54: 28


$(-\infty, \infty)$

Work Step by Step

The domain is the set of all possible values of x for which the value f(x) exists (is defined). For f(x) to be defined, the following conditions must be met: 1. The radicand $\displaystyle \frac{5}{x^{2}+36}$ must not be negative (because of the square root) The numerator is positive. The denominator is $ \geq $36, because $x^{2} \geq 0$, So, it is positive. The first condition is satisfied by all real numbers. 2. The denominator, $x^{2}+36$, must not be zero. We already concluded that $x^{2}+36 \geq 36 > 0$, so this condition is also satisfied by all real numbers. Domain: $\mathbb{R}$ (all real numbers) or $(-\infty, \infty)$
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