Question

A rectangle has a length represented by the function f(x)=x
𝑓
(
𝑥
)
=
𝑥
and a width represented by the function g(x)=x+3
𝑔
(
𝑥
)
=
𝑥
+
3
where both functions are in feet.

Calculate (f⋅g)(x)
(
𝑓
⋅
𝑔
)
(
𝑥
)
and state what it represents.

(1 point)
Responses

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

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

(f⋅g)(x)=x2+3x
(
𝑓
⋅
𝑔
)
(
𝑥
)
=
𝑥
2
+
3
𝑥
; It represents the area of the rectangle in square feet.
(f⋅g)(x)=x2+3x
(
𝑓
⋅
𝑔
)
(
𝑥
)
=
𝑥
2
+
3
𝑥
; It represents the area of the rectan

Answer 1

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

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

Now let's compute \((f \cdot g)(x)\):
\[
(f \cdot g)(x) = f(x) \cdot g(x) = x \cdot (x + 3)
\]
\[
= x^2 + 3x
\]

This result, \(x^2 + 3x\), represents the area of the rectangle in square feet, where \(f(x)\) is the length and \(g(x)\) is the width.

So the correct response is:
\[
(f \cdot g)(x) = x^2 + 3x; \text{ It represents the area of the rectangle in square feet.}
\]