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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q 5.88 (page 547)

For function $f (x) = x^{2} - 5 x - 36$ and $g (x) = x + 4$ Find (a) $(\frac{f}{g}) (x)$ (b) $(\frac{f}{g}) (- 5)$

Short Answer

Expert verified

The solution is (a) $x - 9$

(b) The value at $x = - 5$ is $- 14$

Step by step solution

01

Step 1. Given Information

$f (x) = x^{2} - 5 x - 36$ and $g (x) = x + 4$

02

Part (a) Step 1. Find fgx

$(\frac{f}{g}) (x) = \frac{f (x)}{g (x)} (\frac{f}{g}) (x) = \frac{x^{2} - 5 x - 36}{x + 4} (\frac{f}{g}) (x) = x - 9$

03

Part (b) Step 1. Substitute x=-5

$(\frac{f}{g}) (x) = x - 9 (\frac{f}{g}) (- 5) = (- 5) - 9 (\frac{f}{g}) (- 5) = - 14$

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