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What is the f, if f(f(x)) = 2x^2 -1

  1. Oct 13, 2004 #1
    Ok, I have tried to solve this since yesterday. I tried inverse function, derivative.. still going nowhere. Please help. :rofl:
  2. jcsd
  3. Oct 13, 2004 #2


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    Just try working through it:

    [tex]f\circ f(x) = x^2 \therefore f(x) = x^{\sqrt{2}}[/tex]

    [tex]f\circ f(x) = 2x^2 \therefore f(x) = 2^{\frac{1}{1 + \sqrt{2}}}x^{\sqrt{2}}[/tex]

    edited to add: I've left the rest for you (I think you can obtian the answer this way, but didn't work it all the way through so I can't say for sure).

    edited to add again: actually there doesn't seem to be any easy way to get the answer this way.
    Last edited: Oct 13, 2004
  4. Oct 13, 2004 #3
    Thanks alot, jcsd.
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