Even and odd functions: Difference between revisions

Revision as of 04:03, 16 July 2005

Revision as of 17:04, 11 August 2005

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* The only function which is ''both'' even and odd is the [[constant function]] which is identically zero (i.e., ''f''(''x'') = 0 for all ''x'').

* In general, the [[addition|sum]] of an even and odd function is neither even nor odd; e.g. ''x'' + ''x''².

* The sum of 2two even functions is even, and any constant multiple of an even function is even.

* The sum of 2two odd functions is odd, and any constant multiple of an odd function is odd.

* The [[multiplication|product]] of 2two even functions is an even function.

* The product of 2two odd functions is again an even function.

* The product of an even function and an odd function is an odd function.

* The [[derivative]] of an even function is odd.