karinalo23
Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

If [tex]\( f(x) = 3 - 2x \)[/tex] and [tex]\( g(x) = \frac{1}{x + 5} \)[/tex], what is the value of [tex]\(\left(\frac{f}{g}\right)(8)\)[/tex]?

A. [tex]\(-169\)[/tex]
B. [tex]\(-1\)[/tex]
C. 13
D. 104

Sagot :

GinnyAnswer
To determine the value of [tex]\(\left(\frac{f}{g}\right)(8)\)[/tex] given the functions [tex]\(f(x)=3 - 2x\)[/tex] and [tex]\(g(x)=\frac{1}{x+5}\)[/tex], follow these steps:

1. First, find [tex]\(f(8)\)[/tex]:
[tex]\[ f(x) = 3 - 2x \quad \text{so} \quad f(8) = 3 - 2(8) = 3 - 16 = -13 \][/tex]

2. Next, find [tex]\(g(8)\)[/tex]:
[tex]\[ g(x) = \frac{1}{x+5} \quad \text{so} \quad g(8) = \frac{1}{8+5} = \frac{1}{13} \][/tex]

3. Now, we need [tex]\(\frac{f(8)}{g(8)}\)[/tex]. Substitute the values found:
[tex]\[ \frac{f(8)}{g(8)} = \frac{-13}{\frac{1}{13}} \][/tex]

4. Simplify the fraction:
[tex]\[ \frac{-13}{\frac{1}{13}} = -13 \times 13 = -169 \][/tex]

Therefore, the value of [tex]\(\left(\frac{f}{g}\right)(8)\)[/tex] is [tex]\(-169\)[/tex].

The correct answer is [tex]\(-169\)[/tex].
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.