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Math Help - Inverse Function Question

  1. #1
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    Inverse Function Question

    a) Show that the function f(x)=x^x is increasing on [e^-1,\infty)
    Done this bit

    b) If g is the inverse function f restricted to [e^-1,\infty) show that

    \lim_{x \to \infty} (g(y)ln(ln(y)))/(ln(y))=1

    Hint: Start with the equation y = x^x and take ln of both sides twice

    Just stuck on section b of this question, any help would be great.
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  2. #2
    MHF Contributor
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    I assume it's \lim_{y \to \infty} (g(y)ln(ln(y)))/(ln(y))=1. Note that when y = x^x, y\to\infty is the same as x\to\infty, so \lim_{y\to\infty} gives the same result as \lim_{x\to\infty}. Express ln(y) and ln(ln(y)) through x and replace g(y) by x; then you will have a limit of some expression of x only.
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