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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