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.

(f • g) (3) = 186

Step-by-step explanation:

The area of a rectangle is (length) (width).

Here, (length) = x + 3 and (width) = 12x - 5, and so the area as a function of x is

(f • g) (x) = (x + 3) (12x - 5) = 12x^2 - 5x + 36x - 15.

This simplifies to:

(f • g) (x) = (x + 3) (12x - 5) = 12x^2 + 31x - 15.

Evaluating this function at x = 3, as instructed, we get:

(f • g) (3) = (12) ( - 5) = 12 (3) ^2 + 31 (3) - 15.

Carrying out the indicated operations, we get: 108 + 93 - 15, or

(f • g) (3) = 186