1. 2.3 The Composition of Functions
Find the composition of two functions and the domain of the composition.
Decompose a function as a composition of two functions.
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2. Composition of Functions
Definition:
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3. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Example
Given that f(x) = 3x  1 and g(x) = x2 + x  3, find:
a) b) a)
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4. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Example
Given that f(x) = 3x  1 and g(x) = x2 + x  3, find:
a) b) a)
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

5. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Example
Given that f(x) = 3x  1 and g(x) = x2 + x  3, find:
a) b) b)
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

6. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Example
Given that f(x) = 3x  1 and g(x) = x2 + x  3, find:
a) b) b)
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

7. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley
Example
Given , find the
domain of
Solution:
f (x) is not defined for negative radicands. Since the inputs of are the outputs of g, the domain of consists of all the values in the domain of g for which g(x) is nonnegative.
The domain is
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley