Question

Question
A rectangle has a length represented by the function f(x)=x
and a width represented by the function g(x)=x+3
where both functions are in feet.

Calculate (f⋅g)(x)
and state what it represents.

(1 point)
Responses

(f⋅g)(x)=x2+3x
; It represents the perimeter of the rectangle in feet.
(f⋅g)(x)=x2+3x
; It represents the perimeter of the rectangle in feet.

(f⋅g)(x)=x2+3x
; It represents the area of the rectangle in square feet.
(f⋅g)(x)=x2+3x
; It represents the area of the rectangle in square feet.

(f⋅g)(x)=4x+6
; It represents the perimeter of the rectangle in feet.
(f⋅g)(x)=4x+6
; It represents the perimeter of the rectangle in feet.

(f⋅g)(x)=4x+6
; It represents the area of the rectangle in square feet.
(f⋅g)(x)=4x+6
; It represents the area of the rectangle in square feet.
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Answer 1

To calculate \((f \cdot g)(x)\), we need to multiply the functions \(f(x)\) and \(g(x)\):

Given:
- \(f(x) = x\)
- \(g(x) = x + 3\)

Now we compute \((f \cdot g)(x)\):

\[
(f \cdot g)(x) = f(x) \cdot g(x) = x \cdot (x + 3) = x^2 + 3x
\]

Now, we need to determine what this represents. The product \(f(x) \cdot g(x)\) gives us the area of the rectangle, where \(f(x)\) is the length and \(g(x)\) is the width.

Thus, the correct response is:

\((f \cdot g)(x) = x^2 + 3x; \text{ It represents the area of the rectangle in square feet.}\)