Exploring Composition of Functions in Algebra 2

What is the composition of functions?

• A function applied to another function.

• A function multiplied by another function.

• A function divided by another function.

• A function subtracted from another function.

In the notation f(g(x)), what does it mean?

• f and g are added.

• g is applied to the result of f(x).

• f is applied to the result of g(x).

• f and g are multiplied.

What is the result of f(g(x)) if f(x) = 2x - 1 and g(x) = 3x^2 + 5?

• 6x^2 + 10

• 3x^2 + 5

• 6x^2 + 9

• 2x - 1

In the example with H(x) = x^2 - 2 and G(x) = 4x + 1, what is H(G(x))?

• 4x^2 + 1

• x^2 - 2

• 16x^2 + 8x + 1

• 16x^2 + 8x - 1

What is the first step in finding G(f(-2))?

• Evaluate f(-2).

• Multiply f and G.

• Evaluate G(-2).

• Add f and G.

What is f(-2) if f(x) = x^2 + 3x?

• -2

• 4

• -6

• 2

What is G(-2) if G(x) = 2x - 2?

• 2

• 0

• -4

• -6

In the final example, what happens when you cube the cube root of x?

• You get x^2.

• You get the cube root of x.

• You get x^3.

• You get x.

What is the final result of H(G(x)) if H(x) = x^3 + 4 and G(x) = cube root of x - 4?

• x - 4

• 4

• x^3

• x

What is the simplified form of H(G(x)) in the final example?

• 4

• x - 4

• x^3

• x