Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am encountering functions of real variable with the following property: $$ f(x) = f(1/x) $$ For example, $$ f(x) = \left(x - \frac{1}{x}\right)\log^{3}{x} \qquad x > 0 $$ Is there a name for this property?

share|cite|improve this question
"Symmetric with respect to reciprocation" is how I would call it – Sasha Oct 4 '11 at 19:25
Invariant under inversion – Andrew Oct 4 '11 at 19:27
This is an observation, not a name. If the domain of $f$ consists of positive numbers, then $g(t) = f(e^t)$ is symmetric about the origin. – Srivatsan Oct 4 '11 at 19:33
@SrivatsanNarayanan: I think you mean $f(e^t)$ is symmetric across the $y$ axis. – Shaun Ault Oct 4 '11 at 20:06
@Shaun Ah, yes. You are correct. I thought of it as a function, rather than as a graph on 2-D. In any case, it might be best to say "$g(t)$ is an even function". – Srivatsan Oct 4 '11 at 20:08

Summary of comments:

  • "Invariant under inversion" is a good name for such functions
  • If the domain consists of positive numbers, one can say instead "$t\mapsto f(e^t)$ is even".
share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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