Cool Functional Equation

Algebra Level 3

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

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

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

This is a original problem.

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