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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 62 (page 653)

In the following exercises, find the domain of each function.
$R (x) = \frac{8 x^{2} - 32 x}{2 x^{2} - 6 x - 80}$

Short Answer

Expert verified

The domain is $R - \{- 5, 8\}$

Step by step solution

01

Given Information

$R (x) = \frac{8 x^{2} - 32 x}{2 x^{2} - 6 x - 80}$

02

Step 2. Factor the denominator

Set the denominator zero

$2 x^{2} - 6 x - 80 = 0 2 (x^{2} - 3 x - 40) = 0$

x^{2} - 3 x - 40 = 0 (x - 8) (x + 5) = 0

03

Step 3. Use the Zero Product Property

$(x - 8) = 0 o r (x + 5) = 0 x = 8, - 5$

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