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mac1147_lecture13_2_b - L13 Composite Functions One-to-one...

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168 L13 Composite Functions; One-to-one Functions; Inverse Functions A composite function f g D (read as “ f composed with g ”) is defined by ( )( ) ( ( )) f g x f g x = D . The domain of f g D is the set of all real x in the domain of g for which ( ) g x is in the domain of f . Example : Show a diagram for the composite function ( )( ) ( ( )) f g x f g x = D Similarly we define: ( )( ) ( ( )) g f x g f x = D 169 Example : Let ( ) 5 f x x = and 2 ( ) 2 g x x = . Find: (a) ( )(4) f g = D (b) ( )(9) g f = D (c) Find the composite functions and their domains ( )( ) g f x = D Domain:
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