# Another Functional Equation!

Algebra Level 5

$\large{f(x+y) = f(x) + f(y) + \alpha}$

Let $$f : \mathbb Q \to \mathbb Q$$, where $$\mathbb Q$$ is the set of all rational numbers, be such that the above functional equation holds true for all $$x,y \in \mathbb Q$$. If $$f(\beta) = \alpha$$, find the value of $$f(\alpha)$$ when $$\beta=403, \alpha=2015$$.

Note - $$\alpha, \beta \in \mathbb N$$.

Bonus - Also generalize the value of $$f(\alpha)$$ in terms of $$\alpha$$ and $$\beta$$.

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