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Function Composition
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Effects of Composition on Range
The range of the composition is determined by the values that can take, which depends on the range of and the function .
Composition of Inverses
If and are inverse functions, then and , where and are identity functions on respective sets.
The composition of two functions, where you apply one function to the result of another function.
Associative Property of Function Composition
Function composition is associative, meaning that .
Composition With Bijective Functions
If and are both bijective, then the composition is also bijective.
Non-Commutative Nature of Composition
In general, function composition is not commutative, which means that .
Domain of the Composition
The domain of the composition is the set of all values in the domain of such that is in the domain of .
Identity Function
The identity function, denoted as , is a function that always returns its input: .
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