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Find f(1)

Source: Greek national M.O. 1997, Final Round, problem 2

November 20, 2011

functionalgebra unsolvedalgebra

Problem Statement

Let a function

f : \Bbb{R}^+ \to \Bbb{R}

satisfy: (i)

f

is strictly increasing, (ii)

f(x) > -1/x

for all

x > 0

, (iii)

f(x)f (f(x) + 1/x) = 1

for all

x > 0

. Determine

f(1)