1. ## Adv Calc #2

Need some help on this one.

Let f(x)= x^2 e^x^2, x in R.
Show f^-1 exists and is differentiable on (0, infinity)

Thanks.

2. Originally Posted by taypez
Need some help on this one.

Let f(x)= x^2 e^x^2, x in R.
Show f^-1 exists and is differentiable on (0, infinity)

Thanks.
Theorem: Let $f$ be a one-to-one function on an open interval $I$, and let $J = f(I)$. If $f$ is differentiable at $x_0 \in I$ and if $f'(x_0) \ne 0$, then $f^{-1}$ is differentiable at $y_0 = f(x_0)$ and $\left( f^{-1}\right)'(y_0) = \frac 1{f'(y_0)}$

are those conditions fulfilled here?

now actually showing that the inverse function exists is another story. we have to cross that bridge before we use the above theorem

3. Thanks. This book states that theorem in a slightly different notation that I was not understanding.