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f(2012)=? if f (x + 1) =(1 + f (x))/ (1 - f (x)) , f(1000)=2012

Source: 2012 Swedish Mathematical Competition p1

April 30, 2021
algebrafunctional equationfunctional

Problem Statement

The function ff satisfies the condition f(x+1)=1+f(x)1−f(x)f (x + 1) = \frac{1 + f (x)}{1 - f (x)} for all real xx, for which the function is defined. Determine f(2012)f(2012), if we known that f(1000)=2012f(1000)=2012.
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