# What do you call a function $f$ such that $f(f(x))=x$?

What is the name of the property of a function that yields the original result when done twice in a row:

$$f(f(x)) = x?$$

I'm pretty sure there is a word for these functions, but I haven't been able to find it.

• The are often called involutions (which generally means something that squares to the identity). – Tobias Kildetoft May 9 '16 at 8:01

Such functions are interesting to study, as they are their own inverse $$f^{-1}(x) = f(x)$$
Some examples:$$f(x) = x\\f(x) = \frac{a}{x}\\f(x) = a - x\\f(x) = a + \frac{b}{x-a}$$
• Further examples in $\Bbb R^n$ can be found here – Surb May 9 '16 at 8:12