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.

  • 7
    $\begingroup$ The are often called involutions (which generally means something that squares to the identity). $\endgroup$ – Tobias Kildetoft May 9 '16 at 8:01

A function that has this property is known as an involution.

Such functions are interesting to study, as they are their own inverse $$f^{-1}(x) = f(x)$$

Some examples:$$f(x) = x\\f(x) = \frac{a}{x}\\f(x) = a - x\\f(x) = a + \frac{b}{x-a}$$

| cite | improve this answer | |
  • 3
    $\begingroup$ Further examples in $\Bbb R^n$ can be found here $\endgroup$ – Surb May 9 '16 at 8:12
  • $\begingroup$ Exactly what I was looking for, thanks. $\endgroup$ – Baptiste Wicht May 9 '16 at 8:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.