# Inverse function theorem for 1 variable

1. Sep 19, 2009

### 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?

2. Sep 19, 2009

### Office_Shredder

Staff Emeritus
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?

3. Sep 19, 2009

### Bohrok

4. Sep 19, 2009

### gamitor

5. Sep 19, 2009

### Bohrok

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