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Is there a way to invert a function defined by an integral?


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#21 studiot

studiot

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Posted 20 April 2017 - 08:56 PM

+1 John for showing more patience than I have to spare.


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#22 SFNQuestions

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Posted 21 April 2017 - 02:43 AM

Feel free to define one for me.

The function has no inverse.

If you want a simpler example, try k(x) =integral  of ax .dx

find the inverse where a=0

The x+y function that appears to just be a plane? Do you think that's not invertible in any way? When a=0, the integral gives you a constant line which when inverted gives you simply a vertical line, and to make it functional it only needs to be equivalent to a translated Dirac delta function or limit the range to a finite number. Literally anything that you can recognize as any kind of curve or shape can be flipped over the line y=x, that's really all you need to ask yourself, the rest is simply a matter of domain/range restrictions and whether or not it's in terms of known functions. Matrices are their own group, it has it's own rules. The definition for a bisection or an inversion or invertible does not necessarily have all the same applications and versatility as in functional analysis. Is there any particular reason you continue to completely evade the specific example I provided wherein the end result is already known but it's complex enough to illustrate the application? Honestly this site is so behind, stackexchange and physicsforums answer things so much quicker and with more detail compared to this site and without the cavalier attitude of the academically disappointing precedent set by the staff. 

 

I know it's not one of the examples you specified.

But you have edited your original post to change the goalposts so it's now impossible to tell.

Why did you do that?

Do you realise it looks like intellectual dishonesty?

As an allegedly accredited staff member you should be able to view the edit history, and if you did you'd see I added the example only shortly after the post in order to give context and a more identifiable goal. Do you realize this looks like abuse and thus a lack of integrity?   

 

 

+1 John for showing more patience than I have to spare.

Uh, no one's forcing you to be here, as a sentient being, your frustration is your own choice.  If you don't have the expertise or experience for making progress with this particular technique, go ahead and do something else. 


Edited by SFNQuestions, 21 April 2017 - 03:07 AM.

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#23 John Cuthber

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Posted 21 April 2017 - 05:43 AM

 

As an allegedly accredited staff member you should be able to view the edit history, and if you did you'd see I added the example only shortly after the post in order to give context and a more identifiable goal. Do you realize this looks like abuse and thus a lack of integrity?   

 

 

Just plain wrong, though I take  your point about the timing of the edit..

I'm not a staff member.

 Any point on the plain gets mapped to a line.

or, with the integral every point gets mapped to the same number.

Since it's an infinity to one mapping, it's not invertible.
 

If I say (k(x)= 0 can you tell me what x is?


Edited by John Cuthber, 21 April 2017 - 06:02 AM.

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What's this signature thingy then? Did you know Santa only brings presents to people who click the + sign? -->




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