To find the value of [tex]\((f \cdot g)(-2)\)[/tex], we need to follow a series of steps:
1. Define the Functions:
[tex]\( f(x) = 8 - 10x \)[/tex]
[tex]\( g(x) = 5x + 4 \)[/tex]
2. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = -2 \)[/tex]:
Substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-2) = 8 - 10(-2)
\][/tex]
Simplify the expression:
[tex]\[
f(-2) = 8 + 20 = 28
\][/tex]
3. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = -2 \)[/tex]:
Substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(-2) = 5(-2) + 4
\][/tex]
Simplify the expression:
[tex]\[
g(-2) = -10 + 4 = -6
\][/tex]
4. Multiply [tex]\( f(-2) \)[/tex] and [tex]\( g(-2) \)[/tex] to find [tex]\((f \cdot g)(-2)\)[/tex]:
[tex]\[
(f \cdot g)(-2) = f(-2) \cdot g(-2)
\][/tex]
Substitute the values we found:
[tex]\[
(f \cdot g)(-2) = 28 \cdot -6
\][/tex]
Simplify the multiplication:
[tex]\[
(f \cdot g)(-2) = -168
\][/tex]
Therefore, the value of [tex]\((f \cdot g)(-2)\)[/tex] is [tex]\(-168\)[/tex].
So, the correct answer is:
[tex]\[
-168
\][/tex]
