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

From Calculus

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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]] | ||

+ | * [[Inverse function of odd function is odd]] | ||

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+ | ===Similar facts for even functions=== | ||

+ | * [[Composite of even function with odd function is even]] | ||

+ | * [[Composite of any function with even function is even]] |

## Latest revision as of 13:03, 28 August 2011

## Contents

## Statement

### Statement for two functions

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

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

### Statement for more than two functions

*Fill this in later*