Sure, let's work through the problem step by step.
We are given two functions, [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
f(x) = 3 - 2x
\][/tex]
[tex]\[
g(x) = \frac{1}{x + 5}
\][/tex]
We need to find the value of [tex]\( \left(\frac{f}{g}\right)(8) \)[/tex]. This means we need to calculate [tex]\( \frac{f(8)}{g(8)} \)[/tex].
First, let's find [tex]\( f(8) \)[/tex]:
[tex]\[
f(8) = 3 - 2 \cdot 8
\][/tex]
[tex]\[
f(8) = 3 - 16
\][/tex]
[tex]\[
f(8) = -13
\][/tex]
Next, let's find [tex]\( g(8) \)[/tex]:
[tex]\[
g(8) = \frac{1}{8 + 5}
\][/tex]
[tex]\[
g(8) = \frac{1}{13}
\][/tex]
Now we need to find [tex]\( \frac{f(8)}{g(8)} \)[/tex]:
[tex]\[
\frac{f(8)}{g(8)} = \frac{-13}{\frac{1}{13}}
\][/tex]
To divide by a fraction, we multiply by its reciprocal:
[tex]\[
\frac{-13}{\frac{1}{13}} = -13 \times 13
\][/tex]
[tex]\[
-13 \times 13 = -169
\][/tex]
Therefore, the value of [tex]\( \left(\frac{f}{g}\right)(8) \)[/tex] is:
[tex]\[
\boxed{-169}
\][/tex]
