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Math Help - Adv Calc #2

  1. #1
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    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.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by taypez View Post
    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
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  3. #3
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    Thanks. This book states that theorem in a slightly different notation that I was not understanding.
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