11/12/2013 1 Compositions • Composing functions mean to “implant one function into another” • “F of G” • “Evaluate G and put that value into F” • = ∘ • Graphs of composite functions are complex Compositions Compositions of inverse function must evaluate to x = = Consider the function = −4 and = 0. +2 () =2 0. +2 −4 = +4−4 =
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11/12/2013
1
Compositions
• Composing functions mean to “implant one function into another”• “F of G”• “Evaluate G and put that value into F”• = ∘• Graphs of composite functions are complex
Compositions
Compositions of inverse function must evaluate to x= =Consider the function = − 4 and = 0. + 2( ) = 2 0. + 2 − 4= + 4 − 4=
11/12/2013
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Important Note
The compositional operator (∘) is not the only operation that can bedone on functions. It is permitted to perform the operations of +,−,×÷ can be done with functions.
± = ± ( )= ( ) ( )÷ = ( )
Compositions
Given: = 2 − and = − 1Find:• ∘ 3• ( −2 )• Define the range of the graph of ∘