Functional Equation.

Algebra Level 3

There is a function (polynomial) satisfying, $$g(x).g(y) = g(x) + g(y) + g(xy) - 2$$, for every $$x,y \in \mathbb R$$.

Given that: $$g(2) = 5$$.

Find the value of : $$g(0) + g(1) + g(2) + g(3)$$.

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