Answer:
(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
