Composite of odd functions is odd: Difference between revisions
(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>...") |
No edit summary |
||
| Line 1: | Line 1: | ||
==Statement== | ==Statement== | ||
===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]]. | ||
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. | |||
===Statement for more than two functions=== | |||
{{fillin}} | |||
Revision as of 12:51, 28 August 2011
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