consider the following functions

Question

Find (f ∘ g)(x).

 

Find the domain of (f ∘ g)(x).

 (Enter your answer using interval notation.)

 

Find (g ∘ f)(x).

 

Find the domain of (g ∘ f)(x).

 (Enter your answer using interval notation.)

 

Find (f ∘ f)(x).

 

Find the domain of (f ∘ f)(x).

 (Enter your answer using interval notation.)

 

Find (g ∘ g)(x).

 

Find the domain of (g ∘ g)(x).

 (Enter your answer using interval notation.)

 

Answer 1

f(g(x)) = (7x-3)/(7x) = 1 - 3/(7x)

the domain is all reals except zer0

g(f(x)) = 7 [ x / (x+3) ] - 3

= [7x - 3(x+3)] / 3(x+3)

= [ 7x - 3x - 9]/ (3(x+3))

= [4x-9]/(3(x+3))

the domain is all reals except -3

f(f(x)) = x/(x+3)

---------------- = x/ [ x + 3(x+3)] = x / ( x + 3x+9) = x/(4x+9)

x/(x+3) + 3

the domain is all reals except -9/4

g(g(x)) = 7(7x-3)-3 = 49x - 24; the domain is all reals