A Popular Function, or Constant?

Algebra Level 5

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

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 \(f(x) > 0\). Determine the value of \(f(2015)\).

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