Composite of odd functions is odd: Difference between revisions

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

@@ Line 1: / Line 1: @@
 ==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]].
+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}}
+==Related facts==
+===Similar facts===
+* [[Odd functions form a vector space]]
+* [[Inverse function of odd function is odd]]
+===Similar facts for even functions===
+* [[Composite of even function with odd function is even]]
+* [[Composite of any function with even function is even]]