Let's find 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].
1. Evaluate [tex]\( f(8) \)[/tex]:
[tex]\[
f(8) = 3 - 2 \cdot 8
\][/tex]
[tex]\[
f(8) = 3 - 16
\][/tex]
[tex]\[
f(8) = -13
\][/tex]
2. Evaluate [tex]\( g(8) \)[/tex]:
[tex]\[
g(8) = \frac{1}{8 + 5}
\][/tex]
[tex]\[
g(8) = \frac{1}{13}
\][/tex]
3. Calculate [tex]\(\left( \frac{f}{g} \right)(8)\)[/tex]:
[tex]\[
\left( \frac{f}{g} \right)(8) = \frac{f(8)}{g(8)}
\][/tex]
[tex]\[
\left( \frac{f}{g} \right)(8) = \frac{-13}{\frac{1}{13}}
\][/tex]
4. Simplify the fraction:
[tex]\[
\left( \frac{f}{g} \right)(8) = -13 \times 13
\][/tex]
[tex]\[
\left( \frac{f}{g} \right)(8) = -169
\][/tex]
Therefore, the value of [tex]\(\left( \frac{f}{g} \right)(8)\)[/tex] is [tex]\(\boxed{-169}\)[/tex].
