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 perimeter of the rectangle in feet. (f⋅g)(x)=x^2 +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. (f⋅g)(x)=4x+6 ; 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)=x^2 +3x ; It represents the area of the rectangle in square feet. (f⋅g)(x)=x^2 +3x ; It represents the area of the rectangle in square feet.

Answer 1

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

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

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

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

Distributing \(x\) gives:

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

This expression represents the area of the rectangle, as it is the product of the length and width.

Therefore, the correct interpretation is:

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