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Finding invertible complex function

  1. Mar 1, 2009 #1
    Hi there,
    This is my first time posting on this site. I'm doing Calculus 2 and am stuck on finding whether or not the following functions are invertible in the given intervals and explaining why.

    (a) sechx on [0,infinity)

    --> I solved (a) but (b) and (c) is where I'm stuck.

    (b) cos(lnx) on (0, e^pi)

    (c) e^(x^2)

    Can someone please help?
     
  2. jcsd
  3. Mar 1, 2009 #2

    Tom Mattson

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    You don't have to find the inverse function, you just have to determine if an inverse exists. A necessary condition for invertibility on an interval is that the function is one-to-one on that interval. This condition is met if the function is monotonic on the interval.

    So how would you determine whether a function is monotonic on [itex][0,\infty)[/itex]?
     
  4. Feb 17, 2011 #3
    A function is monotonic if it is strictly increasing or decreasing, correct? Then one would find this info out based on the sign of the first derivative?
     
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