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

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

where "E" is for Euclidean norm
 
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What exactly are you stuck on? It looks pretty straightforward...
 


LCKurtz said:
What exactly are you stuck on? It looks pretty straightforward...
What do you get for the supremum?
 


evagelos said:
What do you get for the 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.
 


I get 6,is it right or wrong??
 


evagelos said:
I get 6,is it right or wrong??

Wrong.
 


LCKurtz said:
Wrong.

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


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

No, it isn't. Why don't you show us your work so we can help you find your mistake.
 


LCKurtz said:
No, it isn't. Why don't you show us your work so we can help you find your mistake.


Sorry,mistake, it should be : (0,5) instead (0,6) and hence the supremum is 5
 
  • #10


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


you are making a mistake read the original post again
 

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