Exploring Composite Functions and Their Domains

What is a composite function?

• A function that is divided by another function

• A function that is added to another function

• A function that is multiplied by another function

• A function that is applied to the result of another function

In the notation F(G(x)), which function is the inner function?

• Both F and G

• G

• F

• X

How do you evaluate F(G(2)) if G(x) = 2x - 1 and F(x) = 3x?

• Add the results of F(2) and G(2)

• Multiply the results of F(2) and G(2)

• Evaluate F(2) first, then use that result in G

• Evaluate G(2) first, then use that result in F

What is the result of F(G(2)) if G(x) = 2x - 1 and F(x) = 3x?

• 6

• 9

• 3

• 12

What is the result of G(F(2)) if G(x) = 2x - 1 and F(x) = 3x?

• 6

• 11

• 3

• 9

What does it mean when we say composite functions are non-commutative?

• F(G(x)) and G(F(x)) are never equal

• F(G(x)) and G(F(x)) are sometimes equal

• F(G(x)) and G(F(x)) are equal only for linear functions

• F(G(x)) and G(F(x)) are always equal

How do you find F(G(x)) in terms of x if G(x) = 2x - 1 and F(x) = 3x?

• Multiply G(x) and F(x)

• Substitute G(x) into F(x)

• Substitute F(x) into G(x)

• Add G(x) and F(x)

What is the result of F(G(x)) if G(x) = 2x - 1 and F(x) = 3x?

• 6x + 3

• 6x - 3

• 2x - 1

• 3x - 1

What is the result of G(F(x)) if G(x) = 2x - 1 and F(x) = 3x?

• 2x - 1

• 3x - 1

• 6x + 1

• 6x - 1

What is the expanded form of (2x + 5)^2 - 1?

• 4x^2 + 10x + 25

• 4x^2 + 10x + 24

• 4x^2 + 20x + 25

• 4x^2 + 20x + 24