mac1105_lecture20_1

# mac1105_lecture20_1 - L20 Composite Functions One-to-one...

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221 L20 Composite Functions; One-to-one Functions A composite function fg D (read as “ f composed with g ”) is defined by () ( ) ( ( ) ) x f g x = D . The domain of D is the set of all real x in the domain of g for which ( ) gx is in the domain of f . Example : Show a diagram for the composite function ( ) ( ( ) ) x f g x = D Similarly we define: ( )( ) ( ( )) gfx g f x = D

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222 Example : Let () 5 fx x = and 2 2 gx x = . Find: (a) ( )(4) fg = D (b) ( )(9) gf = D (c) Find the composite functions and their domains ( ) gfx = D Domain:
223 () ( ) fg x = D Domain: Example : Using the tables, find ( )(2) D and ( )(1) gf D . What is the value of ( )(0) D ? x 1 0 1 x 3 0 2 fx 5 1 3 gx 15 6 0

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224 Example : Find functions f and g such that fgh = D if 32 4 () ( 1 ) hx x x =+ + 2 1 () x =− +
225 Example : An oil spill in the ocean assumes a circular shape with an expanding radius r given by 1 rt =+ , where t is the number of minutes after the measurements are started and r is measured in meters. (a) Find a formula that gives the area A of the circular region as a function of time t .

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mac1105_lecture20_1 - L20 Composite Functions One-to-one...

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