To solve the problem of finding [tex]\((f \cdot g)(-2)\)[/tex] where [tex]\(f(x) = 8 - 10x\)[/tex] and [tex]\(g(x) = 5x + 4\)[/tex], let's follow these steps:
1. Evaluate [tex]\(f(-2)\)[/tex]:
[tex]\[
f(-2) = 8 - 10(-2) = 8 + 20 = 28
\][/tex]
2. Evaluate [tex]\(g(-2)\)[/tex]:
[tex]\[
g(-2) = 5(-2) + 4 = -10 + 4 = -6
\][/tex]
3. Compute the product [tex]\((f \cdot g)(-2)\)[/tex]:
[tex]\[
(f \cdot g)(-2) = f(-2) \cdot g(-2) = 28 \cdot (-6) = -168
\][/tex]
So, the value of [tex]\((f \cdot g)(-2)\)[/tex] is [tex]\(\boxed{-168}\)[/tex].
