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.
by
Akshay Sharma