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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 61 (page 653)

In the following exercises, find the domain of each function.
$R (x) = \frac{3 x^{2} + 15 x}{6 x^{2} + 6 x - 36}$

Short Answer

Expert verified

The domain is $R - \{- 3, 2\}$

Step by step solution

01

Given Information

$R (x) = \frac{3 x^{2} + 15 x}{6 x^{2} + 6 x - 36}$

02

Step 2. Factor the denominator

Set the denominator zero

$6 x^{2} + 6 x - 36 = 0 6 (x^{2} + x - 6) = 0$

6 (x^{2} + x - 6) = 0 6 (x + 3) (x - 2) = 0

03

Step 3. Use the Zero Product Property

$(x + 3) = 0 o r (x - 2) = 0 x = - 3, 2$

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Most popular questions from this chapter

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 writing it as division:

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In the following exercise, perform the indicated operation:

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Solve each rational function inequality and write the solution in interval notation. Given the function $R (x) = \frac{(x + 1)}{(x - 4)},$ find the values of x that make the function less than or equal to 0.

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