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)

a) 9*x + 27

b) 9*x+3

c) 45

d) 21

Step-by-step 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