Let V be the vector space of polynomials in x over R of degree ≤ 3 and define an inner product f. g = f 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 map a : V→ V by a(f)(x) = f(x) + xf'(x) where the f' denotes differentiation. Which of the following holds with respect to this inner product? Select one: O O O a is self-adjoint O a is orthogonal a is 'anti-self adjoint' meaning a* = -a O a Ia, where I denotes the identity map None of the others apply

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