Take the 2-minute tour ×
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.

I have come across a problem which asks to find $f(x)$ such that $f(f(x))=-x$. Nothing I can find has anything pertaining to the composition of two identical functions. Is there a way that I can dissect this in order to help in finding a possible $f(x)$?

share|improve this question
add comment

2 Answers

Here are some possible answers:

  • Multiply by sqrt(-1).

  • Rotate by 90 degrees.

  • Map an even number x to x+1, and an odd number to 1-x.

I don't think it is possible if f is continuous on real numbers.

share|improve this answer
    
I would the Fourier Transform help? If I recall correctly (note that I am 15), the Fourier Transform is just converting a function from a time to a frequency domain. Where would this be applicable to my situation? –  fr00ty_l00ps Nov 8 '13 at 14:26
    
You are right and I am wrong. I will edit my answer. –  apt1002 Nov 9 '13 at 3:10
    
Another question, how would the last two be represented and/or transformed into a formula or equation? –  fr00ty_l00ps Nov 11 '13 at 14:25
    
You could represent the rotation as a matrix. The even/odd one is best left as a list of cases, I reckon. –  apt1002 Nov 13 '13 at 18:44
add comment
up vote 0 down vote accepted

Through late night serendipity and later verification, I have found that $f(x)=ix$ works for all real numbers.

share|improve this answer
add comment

Your Answer

 
discard

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.