Let's solve the problem step by step given the functions [tex]\( f(x) = 8 - 10x \)[/tex] and [tex]\( g(x) = 5x + 4 \)[/tex].
1. Calculate [tex]\( g(-2) \)[/tex]:
We need to find the value of the function [tex]\( g \)[/tex] at [tex]\( x = -2 \)[/tex]:
[tex]\[
g(-2) = 5(-2) + 4 = -10 + 4 = -6
\][/tex]
2. Calculate [tex]\( f(g(-2)) \)[/tex], which is [tex]\( f(-6) \)[/tex]:
Now, we need to find the value of the function [tex]\( f \)[/tex] at [tex]\( x = -6 \)[/tex]:
[tex]\[
f(-6) = 8 - 10(-6) = 8 + 60 = 68
\][/tex]
Therefore, the value of [tex]\((fg)(-2)\)[/tex] is:
[tex]\[
(fg)(-2) = f(g(-2)) = 68
\][/tex]
So, the correct answer is [tex]\( \boxed{68} \)[/tex].
