Ask a New Question
Menu

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)=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.

(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.
Skip to navigation

1 answer

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

  1. \(f(x) = x\)
  2. \(g(x) = x + 3\)

Now, we find \((f \cdot g)(x)\):

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

Now, distribute \(x\):

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

Next, we determine what this represents. The product of the length and width of a rectangle gives us the area of the rectangle.

Thus, we conclude that:

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