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 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)=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)=4x+6
; It represents the area of the rectangle in square feet.

Answer 1

To find \((f \cdot g)(x)\), we multiply the two functions \(f(x)\) and \(g(x)\).

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

The product \((f \cdot g)(x)\) is calculated as follows:

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

Now, let's simplify this:

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

This result represents the area of the rectangle in square feet, as the area of a rectangle is given by the formula \( \text{Area} = \text{Length} \times \text{Width} \).

So, the correct response is:

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