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.

Question

GPT-4o mini · Answer

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.