f(x) = 1 x
g(x) = x^2 − 8x
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x).
(Enter your answer using interval notation.)
Think of (f ∘ g)(x) as meaning f[g(x)], or "f operated on g of x".
Substitute g(x) in for x in f(x).
(f ∘ g)(x) = 1(x^2 - 8)
This composite function is quadratic, (a parabola) so there are not restrictions on the domain.
Find (g ∘ f)(x).
Substitute f(x) in for x in g(x).
(g ∘ f)(x) = (1x)^2 - 8. This is the same as the function above, due to the simplicity of f(x) = 1x
Find the domain of (g ∘ f)(x).
(Enter your answer using interval notation.)
Find (f ∘ f)(x).
(f ∘ f)(x) = 1(1x) = x
Find the domain of (f ∘ f)(x).
(Enter your answer using interval notation.)
(f ∘ f)(x). is a line, so the domain is all reals, again.
Find (g ∘ g)(x).
(g ∘ g)(x) = (x^2 - 8)^2 - 8
Find the domain of (g ∘ g)(x).
(Enter your answer using interval notation.)
The domain is all reals again.
