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May 12th, 2010, 05:23 PM   #1
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Help on an Analysis Question

1. Let g(x) be a fcn that is continuous on its domain and de fined 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.
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May 12th, 2010, 05:43 PM   #2
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Re: Help on an Analysis Question

Use the IVT on to show that there is a point where It follows that at this point,
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May 12th, 2010, 08:28 PM   #3
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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
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May 13th, 2010, 04:18 AM   #4
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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
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May 13th, 2010, 08:26 AM   #5
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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?
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May 13th, 2010, 10:03 AM   #6
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Re: Help on an Analysis Question

NVM, I got it. Thanks!
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