Answer:
A
Step-by-step explanation:
We are given the two functions:
[tex]f(x) = 3x^2 \text{ and } g(x) = x+2[/tex]
And we want to find:
[tex]( f\cdot g)(x)[/tex]
Recall that this is equivalent to:
[tex]\displaystyle (f \cdot g)(x) = f(x) \cdot g(x)[/tex]
Substitute and evaluate:
[tex]\displaystyle \begin{aligned} (f\cdot g)(x) &= (3x^2)(x+2) \\ \\ &= 3x^2(x) + 3x^2(2) \\ \\ &= 3x^3 + 6x^2 \end{aligned}[/tex]
In conclusion, our answer is A.
