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 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 area of the rectangle in square feet.

Answer 1

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

\[ f(x) = x \quad \text{(length)} \] \[ g(x) = x + 3 \quad \text{(width)} \]

Now we calculate:

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

Distributing the \(x\):

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

So, \((f \cdot g)(x) = x^2 + 3x\).

This expression represents the area of the rectangle in square feet, as area is calculated by multiplying the length and width.

Thus, the correct response is:

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