Question

If f(x)= 3x2 and g(x) = x+2, find (f.g)(x).

A. 3x^3 +6x^2
B. 3x^2 +6x
C. 3x^3 +6x
D. x^3+2

Answer 1

A

Explanation:

We are given the two functions:

`f(x) = 3x^2 \text{ and } g(x) = x+2`

And we want to find:

`( f\cdot g)(x)`

Recall that this is equivalent to:

`\displaystyle (f \cdot g)(x) = f(x) \cdot g(x)`

Substitute and evaluate:

`\displaystyle \begin{aligned} (f\cdot g)(x) &= (3x^2)(x+2) \\ \\ &= 3x^2(x) + 3x^2(2) \\ \\ &= 3x^3 + 6x^2 \end{aligned}`

In conclusion, our answer is A.