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 August 6th, 2014, 08:04 AM #1 Newbie   Joined: Aug 2013 Posts: 11 Thanks: 0 Is this function invertible? Hello. How can one know if this Code: Exp[-a Exp[-x b] - c Exp[-x d]] function, or this similar other Code: Exp[-a Exp[-x/b] - c Exp[-x/d]] are invertible?. Or maybe they have a lot of possible solutions? Thank you in advance. Last edited by skipjack; August 6th, 2014 at 09:11 AM.
 August 6th, 2014, 08:12 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra I suspect that they have a global minimum (less than zero) somewhere in $x \lt 0$, so they probably don't have an inverse defined on the whole of the range. You could confirm/deny this by examining the derivative. Such inverses as they do have are unlikely to have a finite representation in standard functions. Last edited by v8archie; August 6th, 2014 at 08:14 AM.
 August 6th, 2014, 09:15 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,966 Thanks: 2216 There are some easy special cases, such as for c = 0.
August 6th, 2014, 06:46 PM   #4
Math Team

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Math Focus: Wibbly wobbly timey-wimey stuff.
Assuming c is not 0, here is one possibility: a = c = 1, b = 2, d = 1.

As you can see the function is not 1 - 1, which is a requirement for the existence of an inverse function.

-Dan
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 August 7th, 2014, 01:02 AM #5 Newbie   Joined: Aug 2013 Posts: 11 Thanks: 0 Thank you very much for your posts. I want to clarify one thing: we suppose the constants a,b,c and d are higher than 0. And I want to ask other regarding v8archie response: Are there any rules to confirm whether the function is invertible or not? Could you give me any reference? Thanks. Last edited by skipjack; August 10th, 2014 at 11:08 AM.

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