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Question Number 129319 by snipers237 last updated on 14/Jan/21

P r o v e t h a t

i f f i s s u c h a s f^{'} (x) = \frac{f (x)}{x (1 - x - f (x))}

a n d f (1) = 0 b u t f ≇ Θ . T h e n

★ f i s t h e u n i q u e b i j e c t i o n f r o m R^{*} t o R a n d

★ \lim_{x \to 0} f (x) = + \infty a n d \lim_{x \to 0} x f (x) = 0

★ \int_{0}^{+ \infty} f^{- 1} (y) d y = ζ (2) = \int_{0}^{1} f (x) d x