DOMAIN OF COMPOSITE FUNCTIONS WORKSHEET

For each of the following problems :

(a) Find f ∘ g and its domain.

(b) Find g ∘ f and its domain.

Problem 1 :

f(x) = x² + 3x; g(x) = 2x - 7

Problem 2 :

f(x) = 6x + 2; g(x) = 7 - x²

Problem 3 :

Problem 4 :

Problem 5 :

f(x) = √(x + 7); g(x) = -5 - x

Problem 6 :

f(x) = √(3 - x); g(x) = 9 - 2x

Answer Key

a) domain of f ∘ g is (-∞, ∞).

(b) domain of g ∘ f is (-∞, ∞).

a) domain of f ∘ g is (-∞, ∞).

(b) domain of g ∘ f is (-∞, ∞).

a) domain of f ∘ g is all real numbers expect 4.

b) domain of g ∘ f is (-∞, -2) ∪ (2, ∞).

a) Domain is all real values.

b) domain of g ∘ f is all real numbers except -5.

a) domain of f ∘ g is (-∞, 2]

b) domain of g ∘ f is [-7, ∞).

a) domain of f ∘ g is [3, ∞).

b) domain of g ∘ f is (-∞, ∞).