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Operations with Functions

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Function Operations Addition: Subtraction: Multiplication: Division:

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Examples: If and Find (f + g)(x) Find (f - g)(x) Find

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Examples: If and Find (f + g)(3) Find (f - g)(0) Find

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Composition OF Functions

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**Definition of composite functions**

Suppose f and g are functions such that the range (output) of g is the subset of the domain (input) of f. Then the composite function can be described by the equation

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**Let’s do an example together.**

• Substitute 2x-3 in for g(x): • Substitute into f(x): Next

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Simplify:

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• Substitute for g(x): • Substitute f(x) into g(x): • Simplify:

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Another example Next

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Try these on your own:

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Answers:

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**Now we will go over how to find a value of composite of functions.**

Find each value. Substitute in g(x). Substitute into g(x). Simplify Next

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Substitute into f(x). Simplify

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**Now you find the values using the same directions as in the last examples.**

Answer: 64 Answer: -5

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EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

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