I'm completly unsure how to tackle this problem

the subject of the following is Linear Transformations.

Given in the text:

....We also have linear transformations on function spaces, such as multiplication operators.

2.5

given that:

and the operation of differentiation

2.6

we also have integration

2.7

note also that

2.8

and

where denotes the space of polynomials in x of degree

QUESTION:

compute

and

and specify the null space and range of both i and D