Combinations of Functions

Question

 Let f(x)=1/x and g(x)=5x+8. Evaluate the following:

1.	(f∘g)(x)	=
2.	(g∘f)(x)	=
3.	(f∘f)(x)	=
4.	(g∘g)(x)	=

Answer 1

f(x) = 1/x

g(x) = 5x +8

(f(x))(g(x)) = (1/x)(5x+8) = 5 + 8/x = (g(x))(f(x))

(f(x))(f(x)) = 1/x^2

(g(x))(g(x)) = (5x+8)^2 = 25x^2 +80x +64

but that's not what you want. you want the composite functions, although it's hard to tell if you're using a small dot as a multiplication symbol or using a small open dot which means composite functions

f(g(x)) = 1/(5x+8)

g(f(x)) = 5/x + 8

f(f(x)) =1/(1/x) = x

g(g(x)) = 5(5x+8)+8 = 25x+48

Answer 2

(f∘g)(x) means f(g(x)) meaning you insert g(x) into f(x):

(f∘g)(x) = f(g(x)) = f(5x + 8) = 1/(5x + 8)

(g∘f)(x) = g(f(x)) = g(1/x) = 5(1/x) + 8 = (5/x) + 8

(f∘f)(x) = f(f(x)) = f(1/x) = 1/(1/x) = x

(g∘g)(x) = g(g(x)) = g(5x + 8) = 5(5x + 8) + 8 = 25x + 48