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)=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 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.
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Answer 1

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

1. Given:

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

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

The result is: \[ (f \cdot g)(x) = x^2 + 3x \]

Now, this represents the area of the rectangle in square feet because area is calculated by multiplying length and width.

Thus, the correct response is: \[ (f \cdot g)(x) = x^2 + 3x; \text{ It represents the area of the rectangle in square feet.} \]