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Inverse function theorem for 1 variable

  1. Sep 19, 2009 #1
    Dear all,

    Does anybody knows any the proof for Inverse Function Theorem for single variable function or link where I can find that proof?

    Thank you in advance
     
  2. jcsd
  3. Sep 19, 2009 #2

    Office_Shredder

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    The statement for a single variable is that if f:R->R is continuously differentiable, and f'(a) is non-zero, f is locally invertible. But if f'(a) is non-zero, it must either be greater than 0 or less than 0. So on some interval around a, f'(a) is always positive or always negative. What can you conclude?
     
  4. Sep 19, 2009 #3
  5. Sep 19, 2009 #4
  6. Sep 19, 2009 #5
    Start with
    [tex]f(f^{-1}(x)) = x[/tex]

    Differentiate both sides, then solve for f-1'(x)
     
  7. Sep 19, 2009 #6
    Thanks a lot!!!
     
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