Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.1 Algebra Essentials - A.1 Assess Your Understanding - Page A11: 72

Answer

$(b)$ and $(d)$

Work Step by Step

The domain of a rational expression is the whole set of real numbers, excluding the numbers that make the denominator equal to zero (since division of zero is not allowed). Here, we exclude $x$ for which the denominator is equal to zero. To find the numbers that will make the denominator zero, set the denominator equal to zero then solve the equation: $ x^{2}-1=0\qquad$ Add $1$ from each side of the equation to obtain: $x^{2}=1$ Take the square root of both sides: $\sqrt{x^2}=\pm\sqrt{1}$ $x=\pm1$ Thus, the numbers that will be excluded from the domain are $-1$ and $1$.. Hence, the answer is $(b)$ and $(d)$.
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