Question

Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) and select the correct answer below:

f(x) = 3x2 + 2

g(x) = x − 8

A. -42
B. -84
C. 42
D. 84

Answer 1

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