Consider the following functions. f(x) = 6x − 5, g(x) = x/2

Question

Consider the following functions.

f(x) = 6x − 5, g(x) = x/2

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(x/2) = 6(x/2) − 5 = 3x − 5/2

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

C) (g ∘ f)(x) = g(f(x)) = g(6x − 5) = (6x − 5)/2 = 3x − 5/2

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

E) (f ∘ f)(x) = f(f(x)) = f(6x − 5) = 6(6x − 5) − 5 = 36x − 35

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

G) (g ∘ g)(x) = g(g(x)) = g(x/2) = (x/2)/2 = x/4

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