Finding the Domain of Function Compositions

Why is it important to consider the domain of both the input and the new function in a composition?

• To find the range of the composition.

• To determine the inverse of the composition.

• To simplify the composition.

• To ensure the composition is defined for all values.

What is the function f(x) in the given example?

• x - 3

• x + 2

• 1/x

• 1/(x + 2)(x - 3)

Which value must be excluded from the domain of f(x) = 1/x?

• x = 2

• x = 1

• x = -1

• x = 0

What is the composition g(f(x)) in the example?

• 1/(x + 2)(x + 3)

• 1/(1/x + 2)(1/x - 3)

• 1/(x + 2)(1/x - 3)

• 1/(1/x + 2)(x - 3)

What equation must be solved to find values that make the first factor in the denominator zero?

• 1/x + 2 = 0

• 1/x - 3 = 0

• x + 2 = 0

• x - 3 = 0

What value of x makes the equation 1/x + 2 = 0 true?

• x = 2

• x = -1/2

• x = -2

• x = 1/2

What value of x makes the equation 1/x - 3 = 0 true?

• x = -3

• x = 3

• x = -1/3

• x = 1/3

Which of the following values must be excluded from the domain of the composition g(f(x))?

• x = 0, -1/2, 1/3

• x = 2, -2, 1/2

• x = -1

• x = 1

How is the domain of the composition g(f(x)) expressed in interval notation?

• (-∞, -1/2) ∪ (-1/2, 1/3) ∪ (1/3, ∞)

• (-∞, 0) ∪ (0, 1/2) ∪ (1/2, 1/3) ∪ (1/3, ∞)

• (-∞, -1/2) ∪ (-1/2, 0) ∪ (0, 1/3) ∪ (1/3, ∞)

• (-∞, -1/3) ∪ (-1/3, 0) ∪ (0, 1/2) ∪ (1/2, ∞)

What is the final step in determining the domain of a composition of functions?

• Finding the range of the composition.

• Finding the inverse of the composition.

• Simplifying the composition.

• Excluding all values that make the denominator zero.