even function

A function f(x) is said to be even (an even function) if f(x) = f(-x) for all x in D , where D is the domain of the function.

Examples of even functions: f(x) = cos x, f(x) = 2, f(x) = x².

See also odd function.

To expand: The property f(x) = f(-x) means that graphs of even functions are symmetric when reflected in the y-axis.

This is a very distinctive feature which allows the evenness of even functions to be recognised at a glance!

The fact that any function can be represented as the sum of an even function and an odd one is very important in many branches of mathematics, most notably in Fourier analysis.