# Given the function: f: (0,1) => (2x+1,4x)

1. Apr 15, 2010

### evagelos

Given the function: f: (0,1) => (2x+1,4x) ,find sup{$$||f(x)||_{E}$$ :xε(0,1)}

where "E" is for Euclidean norm

2. Apr 15, 2010

### LCKurtz

Re: supremum

What exactly are you stuck on? It looks pretty straightforward...

3. Apr 15, 2010

### evagelos

Re: supremum

What do you get for the supremum?

4. Apr 15, 2010

### LCKurtz

Re: supremum

What did you get? The idea here is for you to show us what you have done and we will help you over any trouble spots or verify your work.

5. Apr 15, 2010

### evagelos

Re: supremum

I get 6,is it right or wrong??

6. Apr 15, 2010

### LCKurtz

Re: supremum

Wrong.

7. Apr 15, 2010

### evagelos

Re: supremum

Is it not {$$||f(x)||_{E}$$ :xε(0,1)} =(0,6)??

8. Apr 15, 2010

### LCKurtz

Re: supremum

9. Apr 16, 2010

### evagelos

Re: supremum

Sorry,mistake, it should be : (0,5) instead (0,6) and hence the supremum is 5

10. Apr 16, 2010

### HallsofIvy

Staff Emeritus
Re: supremum

What should be "(0, 5)"???

It looks obvious to me that both components are increasing functions of x and that, as x approaches 1, (2x+1, 4x) approaches (3, 4).

11. Apr 16, 2010

### evagelos

Re: supremum

you are making a mistake read the original post again