Let V be the vector space of polynomials in a over R of degree <3 and define an inner product f. g = f¹ f(x)g(x) dx for all f, g € V. You may assume that this makes V into an inner product space. Define the linear mapa : V→ V by a(f)(x) = f(x) + x f'(x) where the f' denotes differentiation. Which of the following holds with respect to this inner product?

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