Consider the following

Question

f(x) = 1/x, g(x) = 5x+6

(a)

Find the function f ∘ g.

(f ∘ g)(x) =

Find the domain of the function. (Enter your answer using interval notation.)

(b)

Find the function g ∘ f.

(g ∘ f)(x) =

Find the domain of the function. (Enter your answer using interval notation.)

(c)

Find the function f ∘ f.

(f ∘ f)(x) =

Find the domain of the function. (Enter your answer using interval notation.)

(d)

Find the function g ∘ g

(g ∘ g)(x) = 

Find the domain of the function. (Enter your answer using interval notation.)

Answer 1

f(x) = 1/x g(x) = 5x +6

(fog)(x) = f(g(x) = f(5x+6) = 1/(5x+6)

domain is all real numbers except -6/5

the domain is (-infinity, -6/5) U (-6/5, infinity)

(gof)(x) = g(f(x) = g(1/x) = 5(1/x) + 6 = 5/x + 6

domain is any real number except 0

(-infinity, 0) U (0, infinity)

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

domain is all real numbers

(-infinity, + infinity)

(gog)(x) = g(5x+6) = 5(5x+6) + 6 = 25x +30 + 6 = 2x + 36

domain is any real number

(-infinity, + infinity)