The function f(x) = x + 3 represents the length of a rectangle. The function g(x) = 12x − 5 represents the width of the rectangle. Use (f ⋅ g)(3) to determine the area of the rectangle.
186
37
31
6
(f ⋅ g)(3) means to multiply the values of f(3) and g(3) and get the product.
f(3) = 3 + 3 = 6
g(3) = 12(3) - 5 = 31
So, (f ⋅ g)(3) = 6 × 31 = 186.
Therefore, the area of the rectangle is 186 square units.
Answer: 186.
To determine the area of the rectangle using the functions f(x) = x + 3 and g(x) = 12x - 5, we need to find the product of f(3) and g(3), which can be represented as (f ⋅ g)(3).
1. First, let's find f(3) by substituting x=3 into the function f(x) = x + 3.
f(3) = 3 + 3
= 6
2. Next, let's find g(3) by substituting x=3 into the function g(x) = 12x - 5.
g(3) = 12(3) - 5
= 36 - 5
= 31
3. Finally, let's find the product of f(3) and g(3), which can be represented as (f ⋅ g)(3).
(f ⋅ g)(3) = f(3) * g(3)
= 6 * 31
= 186
Therefore, the area of the rectangle is 186.