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May 12th, 2010, 04:23 PM  #1 
Newbie Joined: May 2010 Posts: 6 Thanks: 0  Help on an Analysis Question
1. Let g(x) be a fcn that is continuous on its domain and defined for all real x. Suppose that lim (x> negative infinity) =infinity and lim (x> infinity)= negative infinity. Is there is a value of x such that g(g(x)) = x. 
May 12th, 2010, 04:43 PM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Help on an Analysis Question
Use the IVT on to show that there is a point where It follows that at this point, 
May 12th, 2010, 07:28 PM  #3 
Newbie Joined: May 2010 Posts: 6 Thanks: 0  Re: Help on an Analysis Question
Hi mattpi, Thanks so much for the reply. I was wondering if you could possibly elaborate. IVT on "F(x) minus x"? I'm familiar with the theorem but am having trouble seeing how I can apply it directly given the problem description 
May 13th, 2010, 03:18 AM  #4 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Help on an Analysis Question
You should be able to see from the description of that as If you look at what this means formally, you should be able to define a closed interval such that and The IVT then tells you that there exists an such that 
May 13th, 2010, 07:26 AM  #5 
Newbie Joined: May 2010 Posts: 6 Thanks: 0  Re: Help on an Analysis Question
Ok, great. I can actually see that now, Bolzano's Theorem. Nice! How does that imply that f(f(x))=x?

May 13th, 2010, 09:03 AM  #6 
Newbie Joined: May 2010 Posts: 6 Thanks: 0  Re: Help on an Analysis Question
NVM, I got it. Thanks!


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