Monday, February 21, 2011

Bit of a maths puzzle.


Ugh! This comes out nicely on my blog but looks like crap in Google reader, presumably because the javascript can't run.
Define a function:
\[ f(x) = \frac{2x}{1 - x^2} \] In case that maths layout thing isn't working, that's f(x) = 2x/(1-x^2)
Now, \[ f(0) = 0 \] so that repeats. Also \[ f(\sqrt 3) = -\sqrt 3 \] and \[ f(\sqrt -3) = \sqrt 3 \] so that repeats too.
The question is, what values repeat if you keep applying f to the result? I thought I knew the answer but now I think maybe it's more tricky.
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