Question

For f(x) = 9x and g(x) = x + 3, find the following functions.

a. (f o g)(x)​;
b. (g o f )(x)​;
c. (f o g )(2)​;
d. (g o f )(2)

Answer 1

a) 9*x + 27

b) 9*x+3

c) 45

d) 21

Explanation:

since (f o g)(x) = f (g(x)) , then

a) (f o g)(x) = f (x + 3) = 9*(x+3) = 9*x + 27

similarly

b) (g o f)(x) = g (f(x)) = g ( 9x) = (9*x)+3 = 9*x+3

c) for x=2

(f o g)(2) = 9*2 + 27 = 45

d) for x=2

(g o f )(2) = 9*2 +3 = 21

thus we can see that the composition of functions is not necessarily commutative