Exploring Composition of Functions in AP Precalculus

Mr. Bean teaches AP pre-calculus students about the composition of functions, starting with basic examples and advancing to more complex scenarios. He explains how to determine the domain of composed functions and solve domain-related problems using interval notation. The lesson concludes with a section on decomposing complex functions into simpler components.

What is the first step in composing the function H(x) = F(G(x))?

• Plugging F(x) into G(x)

• Plugging G(x) into F(x)

• Multiplying F(x) and G(x)

• Adding F(x) and G(x)

In the example where F(x) = x^2 - 1 and G(x) = √x, what is F(G(x))?

• x - 1

• x^2 - 1

• x + 1

• √x - 1

When composing functions, what should you do if F(x) has multiple instances of x?

• Multiply G(x) by F(x)

• Add G(x) to F(x)

• Plug G(x) into every instance of x

• Plug G(x) into only one instance of x

What is the domain of the composed function H(x) = F(G(x))?

• The intersection of the domains of F(x) and G(x)

• The domain of G(x)

• The domain of F(x)

• All real numbers

If G(x) = x^2 - 8 and F(x) = x - 1, what is F(G(x))?

• x^2 - 9

• x^2 - 8

• x - 9

• x^2 - 1

What is the domain of the function H(x) = x^2 - 9?

• x ≥ 0

• x ≤ 0

• x ≥ 3 or x ≤ -3

• All real numbers

When decomposing the function √(x^3 + 1), what is the inside function G(x)?

• √x

• x + 1

• x^3

• x^3 + 1

What is the outside function F(x) when decomposing √(x^3 + 1)?

• x + 1

• √x

• x^3 + 1

• x^3

In the function 1/(x^2 + 1), what is the inside function G(x)?

• x + 1

• 1/x

• x^2 + 1

• x^2

What is the outside function F(x) when decomposing 1/(x^2 + 1)?

• x^2 + 1

• x^2

• 1/x

• x + 1