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Function Composition
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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 .
Identity Function
The identity function, denoted as , is a function that always returns its input: .
Composition of Inverses
If and are inverse functions, then and , where and are identity functions on respective sets.
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 .
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 .
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