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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