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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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