Find the basis of kernal and image of a transformation

Suppose that n is a positive integer, and let the transformation be defined by where C(x) is the set of continuous function mapping from to a set M.

Find a basis of kernal(T) and Image(T)

so far:

So I know that we need to find the set

Now, if

we will have

So I need to find the set of function that have that behavior?

Re: Find the basis of kernal and image of a transformation

Quote:

Originally Posted by

**tttcomrader** Suppose that n is a positive integer, and let the transformation

be defined by

where C(x) is the set of continuous function mapping from

to a set M.

Find a basis of kernal(T) and Image(T)

so far:

So I know that we need to find the set

Now, if

we will have

So I need to find the set of function that have that behavior?

This is a separable ODE.

Integrating both sides gives