Question

rectangle has a length represented by the function f (x) = x and a width represented by the function
9 (x) = x + 3 where both functions are in feet.
Calculate (f • g) (x) and state what it represents.
(1 point)
• (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) = x? + 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.

Answer 1

To find \( (f \cdot g)(x) \), we first need to define the functions clearly:

- The length of the rectangle is given by \( f(x) = x \).
- The width of the rectangle is given by \( g(x) = x + 3 \).

Now we compute the product \( (f \cdot g)(x) \):

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

Expanding this expression:

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

This expression represents the area of the rectangle because the area (A) of a rectangle is given by the formula:

\[
A = \text{length} \times \text{width}
\]

So the correct interpretation is:

**(f • g)(x) = x² + 3x; It represents the area of the rectangle in square feet.**