Chapter 4.1, Problem 25E

Let D be the differentiation operator on $P_3$ , and let
$S=\left\{p\in P_3|p(0)=0\right\}$
Show that
(a) D maps $P_3$ onto the subspace $P_2$ , but $D:P_3\to P_2$ is not one−to−one.
(b) $D:S\to P_3$ is not one−to−one but not onto.