Let P₂ (R) be the space of all polynomials of order 2 and f: P₂ (R) → P₂(R) be the linear map defined by: f(1) = 1 + x, f(x)=3-x² and f(x²) = 4+2x - 3x². What is the image of the polynomial a +bx+cr²? Compute f(2-2x+3x²2).

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