Difference between revisions of "Composite of odd functions is odd"

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(Created page with "==Statement== Suppose <math>f</math> and <math>g</math> are fact about::odd functions so that the composite <math>f \circ g</math>...")
 
(Related facts)
 
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==Statement==
 
==Statement==
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===Statement for two functions===
  
 
Suppose <math>f</math> and <math>g</math> are [[fact about::odd function]]s so that the [[fact about::composite of two functions|composite]] <math>f \circ g</math> makes sense. Then, <math>f \circ g</math> is also an [[odd function]].
 
Suppose <math>f</math> and <math>g</math> are [[fact about::odd function]]s so that the [[fact about::composite of two functions|composite]] <math>f \circ g</math> makes sense. Then, <math>f \circ g</math> is also an [[odd function]].
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Note that composition of functions does not commute, so if we can make sense of both <math>f \circ g</math> and <math>g \circ f</math>, these are ''both'' (possibly equal, possibly distinct) odd functions.
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===Statement for more than two functions===
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{{fillin}}
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==Related facts==
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===Similar facts===
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* [[Odd functions form a vector space]]
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* [[Inverse function of odd function is odd]]
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===Similar facts for even functions===
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* [[Composite of even function with odd function is even]]
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* [[Composite of any function with even function is even]]

Latest revision as of 13:03, 28 August 2011

Statement

Statement for two functions

Suppose f and g are odd functions so that the composite f \circ g makes sense. Then, f \circ g is also an odd function.

Note that composition of functions does not commute, so if we can make sense of both f \circ g and g \circ f, these are both (possibly equal, possibly distinct) odd functions.

Statement for more than two functions

Fill this in later

Related facts

Similar facts

Similar facts for even functions