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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 7.80 (page 1069)

For rational function, $f (x) = \frac{x - 1}{x^{2} - 6 x + 5}$ , a)find the domain of the function b) solve f(x) = 4c) find the points on the graph at this function value.

Short Answer

Expert verified

a) The domain is all real numbers except 1 and 5.

b) The solution is $x = \frac{21}{4}$

c) The point is $(\frac{21}{4}, 4)$

Step by step solution

01

(a)Step 1. Given.

The given rational function is $f (x) = \frac{x - 1}{x^{2} - 6 x + 5}$ .

02

Step 2. To find

Find the domain of the function.

03

Step 3. Calculation

For the domain the denominator can not be 0.

$x^{2} - 6 x + 5 鈮� 0 (x - 1) (x - 5) 鈮� 0 x 鈮� 1, 5$

So the domain is all real numbers except 1 and 5.

04

(b)Step 1. Given.

The given rational function is $f (x) = \frac{x - 1}{x^{2} - 6 x + 5}$ .

05

Step 2. To find

Solve $f (x) = 4$ .

06

Step 3. Calculation

$Plug f (x) = 4 inthegivenequationandsolvefor x . 4 = \frac{x - 1}{x^{2} - 6 x + 5} 4 (x^{2} - 6 x + 5) = x - 1 4 x^{2} - 24 x + 20 = x - 1 4 x^{2} - 25 x + 21 = 0 (4 x - 21) (x - 1) = 0 x = \frac{21}{4}, 1 But, x 鈮� 1 . So, x = \frac{21}{4} istheonlysolution.$

07

(c)Step 1. Given.

The given rational function is $f (x) = \frac{x - 1}{x^{2} - 6 x + 5}$ .

08

Step 2. To find

Find the points on the graph at this function value $f (x) = 4$

09

Step 3. Calculation

At those x values in b), $y = 4$ .

So, the point is $(\frac{21}{4}, 4)$ .

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