To determine the value of [tex]\((f \cdot g)(-2)\)[/tex], we first need to evaluate the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] at [tex]\(x = -2\)[/tex].
Let's start by finding [tex]\(f(-2)\)[/tex]:
[tex]\[
f(x) = 8 - 10x
\][/tex]
Substitute [tex]\(x = -2\)[/tex]:
[tex]\[
f(-2) = 8 - 10(-2)
\][/tex]
Calculate the value:
[tex]\[
f(-2) = 8 + 20 = 28
\][/tex]
Next, let's find [tex]\(g(-2)\)[/tex]:
[tex]\[
g(x) = 5x + 4
\][/tex]
Substitute [tex]\(x = -2\)[/tex]:
[tex]\[
g(-2) = 5(-2) + 4
\][/tex]
Calculate the value:
[tex]\[
g(-2) = -10 + 4 = -6
\][/tex]
Now we have [tex]\(f(-2) = 28\)[/tex] and [tex]\(g(-2) = -6\)[/tex].
To find [tex]\((f \cdot g)(-2)\)[/tex], we multiply these two values together:
[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]
Calculate the value:
[tex]\[
(f \cdot g)(-2) = -168
\][/tex]
Thus, the value of [tex]\((f \cdot g)(-2)\)[/tex] is [tex]\(-168\)[/tex].
Therefore, the correct answer is [tex]\(-168\)[/tex].
