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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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Find the domain of .
!ew function
&omain of
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Find the domain of .
/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