My Math Forum Is this function invertible?

 Pre-Calculus Pre-Calculus Math Forum

 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

Joined: May 2013
From: The Astral plane

Posts: 2,266
Thanks: 934

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
Attached Images
 exponential.jpg (16.9 KB, 0 views)

 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.

 Tags function, invertible

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Magnesium Linear Algebra 2 December 11th, 2013 02:09 AM soumita Linear Algebra 3 April 28th, 2013 04:49 PM elifast Algebra 1 October 5th, 2012 03:26 AM tinynerdi Linear Algebra 0 February 20th, 2010 05:58 PM 450081592 Linear Algebra 1 November 28th, 2009 01:32 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top