Sure, let's solve this step-by-step.
Given functions:
[tex]\[ f(x) = 8 - 10x \][/tex]
[tex]\[ g(x) = 5x + 4 \][/tex]
We need to determine the value of [tex]\((f \cdot g)(-2)\)[/tex].
First, let's compute [tex]\( f(-2) \)[/tex]:
[tex]\[ f(-2) = 8 - 10(-2) \][/tex]
[tex]\[ f(-2) = 8 + 20 \][/tex]
[tex]\[ f(-2) = 28 \][/tex]
Next, let's compute [tex]\( g(-2) \)[/tex]:
[tex]\[ g(-2) = 5(-2) + 4 \][/tex]
[tex]\[ g(-2) = -10 + 4 \][/tex]
[tex]\[ g(-2) = -6 \][/tex]
Now, [tex]\((f \cdot g)(-2)\)[/tex] is the product of [tex]\( f(-2) \)[/tex] and [tex]\( g(-2) \)[/tex]:
[tex]\[ (f \cdot g)(-2) = f(-2) \cdot g(-2) \][/tex]
[tex]\[ (f \cdot g)(-2) = 28 \cdot (-6) \][/tex]
[tex]\[ (f \cdot g)(-2) = -168 \][/tex]
So, the value of [tex]\((f \cdot g)(-2)\)[/tex] is [tex]\( -168 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{-168} \][/tex]
