Fixed point

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

A graph of a function with three fixed points

Examples

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