Section 9.5 - Composition of Functions

Composition of Functions = the ____________ of the ____________ function becomes the ____________ for the ____________ function.

• output, first, input, second

• input, second, output, first

• output, second, input, first

• input, first, output, second

Determine (f ∘ g)(x), given f(x) = x² and g(x) = x + 1.

• x² + 1

• (x + 1)²

• x² + 2x + 1

• x² + x

• x^2 + 6

• 6 - x^2

• 4 + x^2

• x^2 - 2

• 4 - (x + 2)^2

• x + 6

• 4 - x^2 + 2

• x^2 + 4

• 0

• 4

• -8

• 8

Example 4: Given f(x) = sqrt{4 - x^2} and g(x) = x^2, what is (f o g)(x)?

• sqrt{4 - (x^2)^2}

• sqrt{4 - x^4}

• sqrt{4 - x^2}

• 4 - x^2

• Domain: [-2, 2], Range: [0, 2]

• Domain: [-2, 2], Range: [0, 4]

• Domain: [-4, 4], Range: [0, 2]

• Domain: [-4, 4], Range: [0, 4]

• N(T(t)) = 20(4t + 2)^2 - 80(4t + 2) + 500

• N(T(t)) = 20t^2 - 80t + 500

• N(T(t)) = 20(4t)^2 - 80(4t) + 500

• N(T(t)) = 20t^2 + 80t + 500

• 1 hour

• 2 hours

• 3 hours

• 4 hours