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**[SOLVED] Rudin 5.2**

## Homework Statement

Suppose f'(x)>0 in (a,b). Prove that f is strictly increasing in (a,b), and let g be its inverse function. Prove that g is differentiable, and that

g'(f(x))=1/f'(x)

when a<x<b.

## Homework Equations

## The Attempt at a Solution

I can prove that f is strictly increasing. I cannot prove that the inverse exists. Do I have to go back to the epsilon-delta definition of the derivative for this or is there some clevel way I can manipulate the limits...