# 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

Solution

Problem 2 :

f(x) = 6x + 2; g(x) = 7 - x2

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

f(x) = √(x + 7); g(x) = -5 - x

Solution

Problem 6 :

f(x) = √(3 - x); g(x) = 9 - 2x

Solution

1)

a) domain of f ∘ g is (-∞, ∞).

(b) domain of g ∘ f is (-∞, ∞).

2)

a) domain of f ∘ g is (-∞, ∞).

(b)  domain of g ∘ f is (-∞, ∞).

3)

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

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

4)

a) Domain is all real values.

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

5)

a)  domain of f ∘ g is  (-∞, 2]

b)  domain of g ∘ f is  [-7, ∞).

6)

a) domain of f ∘ g is [3, ∞).

b) domain of g ∘ f is (-∞, ∞).

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