Consider the following functions. f(x) = 2/x , g(x) = 2x + 6

Question

Consider the following functions.

f(x) = 2/x , g(x) = 2x + 6

A)Find (f ∘ g)(x).

B)Find the domain of (f∘ g)(x).

C)Find (g ∘ f)(x).

D)Find the domain of (g ∘ f)(x)

E)Find (f ∘ f)(x).

F)Find the domain of (f ∘ f)(x).

G)Find (g ∘ g)(x).

H)Find the domain of (g ∘ g)(x).

Answer 1

A) (f ∘ g)(x) = f(g(x)) = f(2x + 6) = 2/(2x + 6) = 1/(x + 3)

B) The domain of (f ∘ g)(x) is all real numbers except x = -3, since division by zero is undefined.

C) (g ∘ f)(x) = g(f(x)) = g(2/x) = 2(2/x) + 6 = 4/x + 6

D) The domain of (g ∘ f)(x) is all real numbers except x = 0, since division by zero is undefined.

E) (f ∘ f)(x) = f(f(x)) = f(2/x) = 2/(2/x) = x

F) The domain of (f ∘ f)(x) is all real numbers except x = 0, since division by zero is undefined.

G) (g ∘ g)(x) = g(g(x)) = g(2x + 6) = 2(2x + 6) + 6 = 4x + 12

H) The domain of (g ∘ g)(x) is all real numbers, since there are no restrictions on the domain of x.