A) When doing function operations, adding the functions (subtracting works the same) means we add each function as given.
(a+b)(x) = a(x) + b(x).
So, a(x) + b(x) = (4x + 9) + (3x - 5)
= 4x + 9 + 3x - 5
= 7x -4
B) It's a similar procedure for the product
(a·b)(x) = a(x)·b(x)
= (4x + 9) · (3x - 5)
= 12x² - 20x - 27x - 45 by FOIL method
= 12x² - 47x - 45
C) We are finding a(b(x)), or the composition of a and b. Here, you are putting a function into a function. The key here is to work inside out.
a(b(x)) = a(3x-5).
Now put 3x - 5 in for x in a(x).
= 4(3x-5) +9
= 12x - 20 + 9
= 12x - 11.
