Even and odd functions: Difference between revisions

Revision as of 19:12, 15 April 2004

Revision as of 04:59, 27 June 2004

Line 29:

===Basic properties===

* The only function which is ''both'' even and odd is the [[constant function]] which is identicallyeverywhere zero (that is, the [[zero|zero function]].

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

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

Line 35:

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

* The product of 2 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.

* The derivative of an odd function is even.