3. Let F be a subfield of complex numbers. Let V be the vector space (over F), consisting of all polynomials, i.e. V = F[r]. Let T: V→ V be the function defined by T: f(x) → (x+1)f'(x). d For example T(x² + x) = (x + 1) . — (x² + x) = (x + 1)(2x + 1) = 2x² + 3x + 1. dr (a) Is T a linear transformation? Give proper reasons. (b) Is T invertible? Give proper reasons.

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