Fixed point

File:Fixed point example.svg

A graph of a function with three fixed points

A value x is a fixed point of a function f if and only if f(x) = x.

Examples

1 is a fixed point of [math]\displaystyle{ x^2 }[/math] because [math]\displaystyle{ 1^2 = 1 }[/math]. Some functions do not have fixed points. For example [math]\displaystyle{ x + 1 }[/math] does not have one because [math]\displaystyle{ x + 1 }[/math] is never equal to x.