Find f ∘ g and g ∘ f. f(x) = x3, g(x) = x2/3

Question

(a)    f∘ g =

(b)    g ∘ f=

Find the domain of each function and each composite function. (Enter your answers using interval notation.)

domain of f =

domain of g =

domain of f ∘ g =

domain of g ∘ f =

Answer 1

f(g(x)) = ((x^2/3))³ = x^{2/3 * 3} = x²

g(f(x)) = ((x³))^2/3 = x^{3 * 2/3} = x²

Domain of f(x) is (-∞, ∞)

Domain of g(x) is (-∞, ∞)

Domain of both composit functions (-∞, ∞)