Let's solve the problem step-by-step.
We are given two functions: [tex]\( f(x) = 3 - 2x \)[/tex] and [tex]\( g(x) = \frac{1}{x+5} \)[/tex]. We need to find the value of [tex]\( \left(\frac{f}{g}\right)(x) \)[/tex] at [tex]\( x = 8 \)[/tex].
1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 8 \)[/tex]:
[tex]\[
f(8) = 3 - 2 \cdot 8 = 3 - 16 = -13
\][/tex]
2. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 8 \)[/tex]:
[tex]\[
g(8) = \frac{1}{8 + 5} = \frac{1}{13} \approx 0.07692307692307693
\][/tex]
3. Find [tex]\( \left(\frac{f}{g}\right)(x) \)[/tex] at [tex]\( x = 8 \)[/tex]:
[tex]\( \frac{f(8)}{g(8)} \)[/tex]:
[tex]\[
\left( \frac{f}{g} \right)(8) = \frac{f(8)}{g(8)} = \frac{-13}{\frac{1}{13}} = -13 \cdot 13 = -169
\][/tex]
Thus, the value of [tex]\( \left(\frac{f}{g}\right)(8) \)[/tex] is [tex]\(-169\)[/tex]. So, the correct answer is:
[tex]\[
-169
\][/tex]
