Editing Even and odd functions (section)

==Basic properties==

===Uniqueness===
* If a function is both even and odd, it is equal to 0 everywhere it is defined.
* If a function is odd, the [[absolute value]] of that function is an even function.

===Addition and subtraction===
* The [[addition|sum]] of two even functions is even.
* The sum of two odd functions is odd.
* The [[subtraction|difference]] between two odd functions is odd.
* The difference between two even functions is even.
* The sum of an even and odd function is not even or odd, unless one of the functions is equal to zero over the given [[Domain of a function|domain]].

===Multiplication and division===
* The [[multiplication|product]] and [[Division (mathematics)|quotient]] of two even functions is an even function.
** This implies that the product of any number of even functions is also even.
** This implies that the [[reciprocal function|reciprocal]] of an even function is also even.
* The product and quotient of two odd functions is an even function.
* The product and both quotients of an even function and an odd function is an odd function.
** This implies that the reciprocal of an odd function is odd.

===Composition===
* The [[function composition|composition]] of two even functions is even.
* The composition of two odd functions is odd.
* The composition of an even function and an odd function is even.
* The composition of any function with an even function is even (but not vice versa).

===Inverse function===
* If an odd function is [[inverse function|invertible]], then its inverse is also odd.