04 Composition Functions

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Composition ofFunctions


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The Composition

Function This is read “f circle g” or "f of g of x" andmeans to copy the f function down butwherever you see an x, substitute in the g

function.


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The Composition

Function This is read “g circle f” or “g of f of x"and means to copy the g function downbut wherever you see an x, substitute inthe f function.

!ote


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The Composition

Function This is read “f circle f” or “f of f of x" andmeans to copy the f function down butwherever you see an x, substitute in thef function. #$o sub the function intoitself%


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The Domain of the CompositionFunction The domain of is the set of all numbers inthe domain of such that is in the domain of .

The domain of g is x 1

We also have to worry about any “ illegals ” in this compositionfunction, specifically dividing by 0. This would mean that so thedomain of the composition would be combining the tworestrictions .

&omain of

( ) ( ) 11

−== x x g

x

x f

1

1

−

=

x g f


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The Domain of the CompositionFunction

'. Find the domain of theinput (inside function. #&)!*T

F)+ -T T /$0%1. Find the domain of the new

function after performing thecomposition.

2. et the intersection of ' and 1.


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Find the domain of .

/nside function !ew function

&omain of


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!ew function

&omain of


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/nside function !ew function

&omain of


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$3 $olve for the following

and 4nd its domain.


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!ew function

&omain of


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!ew function

&omain of


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!ew function

&omain of


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!ew function

&omain of

04 Composition Functions

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