Question: (a) Prove that L[p] = p + p defines an invertible linear map on the space P(2) of quadratic polynomials. Find a formula for its

(a) Prove that L[p] = p′ + p defines an invertible linear map on the space P(2) of quadratic polynomials. Find a formula for its inverse.
(b) Does the derivative D[p] = p′ have either a left or a right inverse on P(2)?

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