For this case we have the following functions:
[tex]f(x) = 3x^2 + 2
g(x) = x - 8[/tex]
Multiplying both functions we have:
[tex](f * g)(x) = f(x)*g(x)
(f * g)(x) = (3x^2 + 2)*(x - 8)[/tex]
By doing distributive property we have:
[tex](f * g)(x) = (3x^3 + 2x) + (-24x^2 - 16)
[/tex]
Finally, by rewriting we have:
[tex](f * g)(x) = 3x^3 - 24x^2 + 2x - 16
[/tex]
Then, evaluating for x = 2 we have:
[tex](f * g)(2) = 3(2)^3 - 24(2)^2 + 2(2) - 16
(f * g)(2) = -84[/tex]
Answer:
B. -84
