Hey guys.

I've got the following problem:

Let og let be defined by :

(a) Show thatDone that already.

(b) Show that is injective

(Hint: When is given by monotonic?)

(c)... some more questions.

I've already found the solution to (a), but I cant quite figure out how to solve (b). This is pretty much what I've tried so far:

For to be injective, the following has to be true : .

So, for proof by contradiction, we assume that for a pair we have that .

Since we have that (1).

But since we have that .

According to (1) we know that so must be the case.

From here I dont know exacly where to go. I can see that I'm not really using the hint.

I know that all monotonic functions are injective, but how can I prove that f is monotonic?

I can see by visualization that f will be monotonic, because x is defined to be positive, but how do I prove that rigorously?

Thanks for your help guys.

Morten