Monday, October 19, 2009

f(f(x)) = x^2

Find a real function f so that f(f(x)) = x^2 for all x.

1 comment:

  1. How about f(x) = |x|^\sqrt{2}?
    Since we take the absolute value before exponentiating to an irrational power, f is defined for each real number x.
    Also, f(f(x)) = ||x|^\sqrt{2}|^\sqrt{2} = (|x|^\sqrt{2})^sqrt{2} = x^2.

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