A rectangle has a length represented by the function f(x)=x

Question

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

Answer 1

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

Given:

• \(f(x) = x\) (length of the rectangle)
• \(g(x) = x + 3\) (width of the rectangle)

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

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

Now, this product represents the area of the rectangle because the area \(A\) is calculated as \(A = \text{length} \times \text{width}\).

Therefore, the correct response is:

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