Determining the Domain of Quotient and Composite Functions

The video tutorial explains how to find the domain of different function compositions, including F divided by G, F of G of X, and G of F of X. It covers the restrictions on domains due to division by zero and negative values under square roots, and demonstrates how to express these domains using interval notation. The tutorial also provides step-by-step solutions to determine the domain of composite functions, ensuring all restrictions are considered.

What is the first step in finding the domain of F(x) divided by G(x)?

• Graph the functions.

• Identify the restrictions based on the numerator.

• Identify the restrictions based on the denominator.

• Combine the functions.

Why can't X be zero in the function F(x) divided by G(x)?

• Because it would make the function undefined.

• Because it would make the function negative.

• Because it would make the denominator zero.

• Because it would make the numerator zero.

What is the domain of the quotient function F(x) divided by G(x)?

• (-∞, 3) ∪ (3, ∞)

• (0, ∞)

• (-∞, 0) ∪ (0, ∞)

• (0, 3) ∪ (3, ∞)

What must the domain of F(G(x)) include?

• No restrictions

• Only the restrictions of F(x)

• The restrictions of both F(x) and G(x)

• Only the restrictions of G(x)

What is the domain of a quadratic function?

• Negative numbers only

• Positive numbers only

• All real numbers

• Non-zero numbers

What is the restriction for the composite function F(G(x))?

• X must be negative

• X must be positive

• X squared minus X minus 6 must be greater than zero

• X squared minus X minus 6 must be less than zero

What values of X make the quadratic equation (X squared - X) - 6 equal to zero?

• X = 4 and X = -4

• X = 1 and X = -1

• X = 3 and X = -2

• X = 2 and X = -3

What is the domain of the composite function F(G(x))?

• (-∞, -2) ∪ (3, ∞)

• (0, 3) ∪ (3, ∞)

• (-∞, 0) ∪ (0, ∞)

• (0, ∞)

What is the initial restriction for the domain of G(F(x))?

• X must be greater than zero

• X must be equal to zero

• X must be a real number

• X must be less than zero

What is the domain of the composite function G(F(x))?

• (-∞, ∞)

• (0, 3)

• (0, ∞)

• (-∞, 0)