In the vector space C (a, b] of infinitely differentiable functions on the interval [a, b], consider

In the vector space Cˆž (a, b] of infinitely differentiable functions on the interval [a, b], consider the derivative transformation D and the definite integral transformation I defined by

(a) Compute (DI) (f) = D(I(f)).
(b) Compute (I D) (f) = 1(D(f)).
(c) Do these transformations commute? That is to say, is it true that (Di)(= (1 DX f) for all vectors f in the space?

Transcribed Image Text:

D(f)(x)f'(x) and ()(x)f(dr