Chapter 4.2, Problem 73E

To determine

To check: whether the linear transformation $T\left(f\left(t\right)\right)={\displaystyle \underset{0}{\overset{t}{\int }}f\left(x\right)dx}$ is an isomorphism from $P_{n-1}$ to $Z_n$ , where $Z_n$ is the set of all those polynomials that have at most degree n and $f\left(0\right)=0$ .