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: 73

Answer

$(b),\ (c),$ 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^{3}-x=0\qquad$ Factor the binomial by factoring out $x$ to obtain: $x(x^{2}-1)=0$ Factor the difference of two squares using the formula $a^2-b^2=(a-b)(a+b)$ to obtain: $x(x-1)(x+1)=0$ Solve the equation using the Zero-Product Property by equating each factor to zero, then solve each equation to obtain: \begin{align*} x&=0 &\text{or}& &x-1=0& &\text{or}& &x+1=0\\ x&=0 &\text{or}& &x=1& &\text{or}& &x=-1 \end{align*} Thus, the numbers that will be excluded from the domain are $0$, $-1$, and $1$.. Hence, the answer is $(b)$, $(c)$, and $(d)$.
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