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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. 233 (page 695)

For rational function, $f (x) = \frac{2 - x}{x^{2} - 7 x + 10}$ ,
a) find the domain of the function
b) solve $f (x) = 2$ .
c) find the points on the graph at this function value.

Short Answer

Expert verified

a) The domain is all real numbers except $5, 2$ .

b) The solution is $x = 4.5$ .

c) The point is $(4.5, 2)$ .

Step by step solution

01

(a)Step 1. Given

The given function is $f (x) = \frac{2 - x}{x^{2} - 7 x + 10}$ .

02

Step 2. To find

Find the domain of the function.

03

Step 3. Calculation

For the domain, the denominator can not be 0.

$x^{2} - 7 x + 10 鈮� 0 (x - 5) (x - 2) 鈮� 0 x 鈮� 5, 2$

So the domain is all real numbers except 5 and 2.

04

(b)Step 1. Given

The given function is $f (x) = \frac{2 - x}{x^{2} - 7 x + 10}$ .

05

Step 2. To find

Solve $f (x) = 2$

06

Step 3. Calculation

Set the given equation equal to 2 and solve for x.

$\frac{2 - x}{x^{2} - 7 x + 10} = 2 2 - x = 2 (x^{2} - 7 x + 10) 2 - x = 2 x^{2} - 14 x + 20 2 x^{2} - 13 x + 18 = 0 2 x^{2} - 4 x - 9 x + 18 = 0 2 x (x - 2) - 9 (x - 2) = 0 (x - 2) (2 x - 9) = 0 x = 2, \frac{9}{2} But x 鈮� 2, so x = \frac{9}{2} = 4.5$

07

(c)Step 1. Given

The given function is $f (x) = \frac{2 - x}{x^{2} - 7 x + 10}$ .

08

Step 2. To find

Find the points on the graph at this function value.

09

Step 3. Calculation

The value of x is 4.5.

The value of y is 2.

So, the point is $(4.5, 2)$

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Most popular questions from this chapter

In the following exercises, divide the rational expressions.

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