Let

*f*(

*x*) be a real-valued function of a real variable. Then

*f* is

**even** if the following equation holds for all

*x* in the domain of

*f*:

.

Again, let

*f*(

*x*) be a real-valued function of a real variable. Then

*f* is

__odd__ if the following equation holds for all

*x* in the domain of

*f*:

.

(1)

. Therefore, this function is

__even.__
(2)

The quotient of two even functions is an even function.

The quotient of two odd functions is an even function.

The quotient of an even function and an odd function is an odd function.