
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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]] Code: Exp[a Exp[x/b]  c Exp[x/d]] 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: 7,663 Thanks: 2642 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: 20,746 Thanks: 2133 
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: 2,194 Thanks: 897 Math Focus: Wibbly wobbly timeywimey 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 
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  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Why Isn't This Matrix Invertible?  Magnesium  Linear Algebra  2  December 11th, 2013 02:09 AM 
Transformation is not invertible  soumita  Linear Algebra  3  April 28th, 2013 04:49 PM 
Let f be an invertible function, and g = f^1....  elifast  Algebra  1  October 5th, 2012 03:26 AM 
T: V to V and [T]_B is invertible  tinynerdi  Linear Algebra  0  February 20th, 2010 05:58 PM 
Show that A must be invertible  450081592  Linear Algebra  1  November 28th, 2009 01:32 AM 