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

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In summary, the conversation is about finding the supremum of the Euclidean norm of the function f: (0,1) => (2x+1, 4x) in the interval (0,1). The correct answer is 5, as both components of the function are increasing and approach (3,4) as x approaches 1. The mistake made by the original poster was using (0,6) instead of (0,5).
  • #1
evagelos
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Given the function: f: (0,1) => (2x+1,4x) ,find sup{[tex]||f(x)||_{E}[/tex] :xε(0,1)}

where "E" is for Euclidean norm
 
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  • #2


What exactly are you stuck on? It looks pretty straightforward...
 
  • #3


LCKurtz said:
What exactly are you stuck on? It looks pretty straightforward...
What do you get for the supremum?
 
  • #4


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.
 
  • #5


I get 6,is it right or wrong??
 
  • #6


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

Wrong.
 
  • #7


LCKurtz said:
Wrong.

Is it not {[tex]||f(x)||_{E}[/tex] :xε(0,1)} =(0,6)??
 
  • #8


evagelos said:
Is it not {[tex]||f(x)||_{E}[/tex] :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.
 
  • #9


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
 

1. What is the domain and range of the given function?

The domain of the function is (0,1) and the range is (2,4). This means that the function takes in values between 0 and 1 and outputs values between 2 and 4.

2. Is this function continuous?

Yes, this function is continuous. This means that the graph of the function has no breaks or gaps and can be drawn without lifting the pencil from the paper.

3. What is the slope of the function?

The slope of the function is represented by the coefficient of x, which is 2. This means that for every increase of 1 in the input, the output increases by 2.

4. Is this function one-to-one?

Yes, this function is one-to-one. This means that each input has a unique output. It can be graphically represented as a straight line passing through all points in the range.

5. How can this function be used in real-world applications?

This function can be used in various real-world applications such as calculating the growth rate of a population or the depreciation of an asset over time. It can also be used in economics to represent the relationship between demand and price.

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