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ch.10 Compositions, Inverses, and Combinations of Functions

ch.10 Compositions, Inverses, and Combinations of Functions...

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Chapter 10 Compositions, Inverses, and Combinations of Functions 10.1 Composition of Functions
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Key Points Finding the composition of two functions numerically, graphically and symbolically Interpreting the composition of two functions Decomposing a function
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Formulas for Composite Functions Example 1 Let p ( x ) = cos x + 1 and q ( x ) = x 2 + 2. a. Find a formula in terms of x for r ( x ) = p ( q ( x )). b. Find a formula s ( x ) = p(q(q(x )). c. Find a formula t ( x ) = q ( p ( x )). Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally
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Decomposition of Functions Example 4 Let h ( x ) = f ( g ( x )) = . Find possible formulas for f ( x ) and g ( x ). Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally 1 2 + x e
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22,36,52,54
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Composition of Functions The function f ( g ( t )) is said to be a composition of f with g . The function f ( g ( t )) is defined by using the output of the function g as the input to f . The function f ( g ( t )) is only defined for values in the domain of g whose g ( t ) values are in the domain of f . The function f ( g ( t )) is said to be a composition of f with g . The function f ( g ( t )) is defined by using the output of the function g as the input to f . The function f ( g ( t )) is only defined for values in the domain of g whose g ( t ) values are in the domain of f . Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally
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Chapter 10 Compositions, Inverses, and Combinations of Functions 10.2 Invertibility and Properties of Inverse Functions
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