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Let the equation (a-1) x^2=x(2 b+3) be s...

Let the equation `(a-1) x^2=x(2 b+3)` be satisfied by three distinct values of `x`, where `a, b in R`, If `f(x)=(a-1) x^3+(2 b+3) x^2+2 x+1`, and `f(g(x))=6 x-7` where `g(x)` is a linear function then find the value of `g^prime(2012)`.

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