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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 59 (page 653)

In the following exercises, find the domain of each function.
$R (x) = \frac{x^{3} - 2 x^{2} - 25 x + 50}{x^{2} - 25}$

Short Answer

Expert verified

The domain is $R - \{- 5, 5\}$

Step by step solution

01

Given information

$R (x) = \frac{x^{3} - 2 x^{2} - 25 x + 50}{x^{2} - 25}$

We have to find the domain of the given rational function.

02

Factor the denominator

Set denominator zero

x^{2} - 25 = 0 (x - 5) (x + 5) = 0

03

Use the Zero Product Property

$(x - 5) = 0 o r (x + 5) = 0 x = 5, - 5$

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Most popular questions from this chapter

Simplify the rational expression $\frac{12 p - 240}{5 p - 100} .$

Check whether the points $y = - 6, y = 4$ are the solutions of the equation $\frac{y}{y + 6} = \frac{72}{y^{2} - 36} + 4$ or not.

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For the following exercises, perform the indicated operations.
$\frac{12 p^{2} + 3 p}{p + 3} \div \frac{p^{2} + 2 p - 63}{p^{2} - p - 12} . \frac{p - 7}{9 p^{3} - 9 p^{2}}$

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