12/22/2009, 07:28 AM
It is not injective. You can prove this by counterexample: f(1/4)=f(1/2).
Not only that, but I would go so far as to say that all values between 1/e^1/e and 1 are not injective, even though I haven't really tried to prove it by seeing if the function x^x is made of "monotonic pieces" or not.
Not only that, but I would go so far as to say that all values between 1/e^1/e and 1 are not injective, even though I haven't really tried to prove it by seeing if the function x^x is made of "monotonic pieces" or not.
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