(b) Show that the derivative D[f(x)] = f′(x) defines an invertible linear transformation on this vector space, and determine its inverse. (c) Generalize your result in part (b) to the...

(b) Show that the derivative D[f(x)] = f′(x) defines an invertible linear transformation on this vector space, and determine its inverse.


(c) Generalize your result in part (b) to the infinite-dimensional vector space consisting of all functions of the form p(x)ex, where p(x) is an arbitrary polynomial.