Inverse function theorem for 1 variable

[gamitor]

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

 

[Office_Shredder]

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?

 

[Bohrok]

Are you looking for the proof to

where b = f(a) as shown here?
http://en.wikipedia.org/wiki/Inverse_function_theorem

 

[gamitor]

Are you looking for the proof to

where b = f(a) as shown here?
http://en.wikipedia.org/wiki/Inverse_function_theorem

yes, exactly, but I cannot find anywhere the proof for single variable functions, do you know where it is?

 

[Bohrok]

Start with
$$f(f^{-1}(x)) = x$$

Differentiate both sides, then solve for f^-1'(x)

 

[gamitor]

Start with
$$f(f^{-1}(x)) = x$$

Differentiate both sides, then solve for f^-1'(x)

Thanks a lot!