The length and width of a rectangle are given by f(x) = 3x2 – 2x and g(x) = 2x – 3, where x > 2. What is f ⋅ g and what does its value represent?

A. (f ⋅ g)(x) = 12x2 – 40x + 33; the area of the rectangle
B. (f ⋅ g)(x) = 12x2 – 40x + 21; the perimeter of the rectangle
C. (f ⋅ g)(x) = 6x3 – 13x2 + 6x; the area of the rectangle
D. (f ⋅ g)(x) = 6x3 – 9x2 + 2x; the area of the rectangle

C

Step-by-step explanation:

We are multiplying f(x) and g(x), which are the length and width. The area of a rectangle is a=l*w, so we can eliminate choice B.

Now, we have to find what f(x) * g(x) is

 f(x) * g(x)

f(x) is 3x^2-2x and g(x) is 2x-3, so we can substitute them in

(3x^2-2x)*(2x-3)

Use FOIL to find the answer

F: 3x^2*2x= 6x^3

O: 3x^2* -3 = -9x^2

I: -2x*2x= -4x^2

L: -2x*-3= 6x

6x^3-9x^2-4x^2+6x

Combine like terms

6x^3-13x^2+6x

So, we know that f(x) *g(x) is 6x^3-13x^2+6x, and that it is the area (l*w), so choice C is correct.

19

step-by-step explanation:

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d