A simple functional equation

Algebra Level 4

Let \( f(x) \) be a function that satisfies

\[f(2014 + x) = f(2014 - x) .\]

If \( f \) has exactly \( 3 \) roots being \( \alpha, \beta, \gamma \), what is the value of \( \alpha + \beta + \gamma ?\)

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