A rectangle has a length represented by the function f(x)=x and a width represented by the function g(x)=x+3

Question

where both functions are in feet.
Calculate (f⋅g)(x) and state what it represents.
Responses:
(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 area of the rectangle in square feet.

(f⋅g)(x)=x2+3x; 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 \( f(x) \) and \( g(x) \):

• \( f(x) = x \)
• \( g(x) = x + 3 \)

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

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

Distributing \( x \):

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

Now, let's interpret what this represents. The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). Here:

• Length is represented by \( f(x) = x \)
• Width is represented by \( g(x) = x + 3 \)

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

Therefore, the correct answer is:

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