Compare and Predict

Algebra Level 4

Let ff be a function with domain R\mathbb{R}.

If f(x+2)(1f(x))=1+f(x)f(x+2)\big(1-f(x)\big)=1+f(x) and f(1)=2016f(1)=2016, find the value of f(2017)f(2017).


Notation: R\mathbb{R} denotes the set of real numbers.

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