Combining Function Types in Context Quick Check

Question

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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 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 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)=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.
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Answer 1

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

1. \(f(x) = x\)
2. \(g(x) = x + 3\)

Now, we compute the product:

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

This result, \(x^2 + 3x\), represents the area of the rectangle in square feet, since the area \(A\) is given by the formula \(A = \text{length} \cdot \text{width}\).

So the correct response is:

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