Is there a bijection $f:\mathbb R^+\to\mathbb R^+$ s.t. $f'(x)=f^{-1}(x)$?

Asked Jun 17 '13 at 02:31

Active Jun 17 '13 at 02:31

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Is there a bijection $f:\mathbb R^+\to\mathbb R^+$ s.t. $f'(x)=f^{-1}(x)$?

And if there is, can I prove uniqueness? This problem troubles me.

asked Jun 17 '13 at 02:31

user2438168

Well, what I got out of math club was that this does exist, $f(x)=\phi^{-\frac\phi{\phi+1}}x^\phi$, but not sure how I was meant to determine that, or find uniqueness. – user2438168 Jun 17 '13 at 02:37

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