The regular rules of arithmetic apply to function values. Addition and multiplication are commutative, but subtraction and division are not.
The ring operator, signifying a function of a function, is not commutative, either. A simple example can illustrate this:
f(x) = 3
g(x) = x²
(f◦g)(x) = f(g(x)) = f(x²) = 3
(g◦f)(x) = g(f(x)) = g(3) = 3² = 9 . . . . . not equal to 3
The only appropriate choice for Question 19 is ...
A. (f+g)(x) = (g+f)(x)
