Cool Functional Equation

Algebra Level 3

\[\large{f(f(x)) = f(x) + x}\]

Let \(f : \mathbb{R} \to \mathbb{R}\) be a continuous function such that the above equation is satisfied for all \(x \in \mathbb{R}\), and for all \(x > 0\), we have \(f(x) > 0.\)

If \( f(1)=2014,\) find \(f(2015).\)

This is a original problem.
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