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].
