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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 60 (page 653)

In the following exercises, find the domain of each function.
$R (x) = \frac{x^{3} + 3 x^{2} - 4 x - 12}{x^{2} - 4}$

Short Answer

Expert verified

The domain is $R - \{- 2, 2\}$

Step by step solution

01

Given Information

$R (x) = \frac{x^{3} + 3 x^{2} - 4 x - 12}{x^{2} - 4}$

02

Step 2. Factor the denominator

Set denominator zero

x^{2} - 4 = 0 (x - 2) (x + 2) = 0

03

Step 3. Use the Zero Product Property

$x - 2 = 0 o r x + 2 = 0 x = 2, - 2$

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Most popular questions from this chapter

The distance a moving body travels, $d$ , varies directly with the time, $t$ , it moves. The train travels 100 miles in 2 hours.

Write the equation that relates $d a n d t$ .
How many miles would it travel in 5 hours?

For the following exercises, find $R (x) = f (x) g (x)$ where $f (x) a n d g (x)$ are given.

$f (x) = \frac{x^{2} - 2 x}{x^{2} + 6 x - 16} a n d g (x) = \frac{x^{2} - 64}{x^{2} - 8 x}$

Simplify the complex rational expression by using the LCD:

$\frac{\frac{2}{x - 7} - \frac{1}{x + 7}}{\frac{6}{x + 7} - \frac{1}{x^{2} - 49}}$

In the following exercises, find the domain of each function.

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

Divide the rational expression $\frac{3 y^{2} - 12 y - 63}{4 y + 3} \div (6 y^{2} - 42 y)$

See all solutions

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