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Inverse of the natural logarithms

  1. Oct 31, 2004 #1
    Hi Guys, i am new to this forums and my english is poor, but i will do my best.

    I got stuck with this problem, i think it's quite easy, but i get the wrong answer :frown:

    F(x) = ln(1+e^x)

    1. Show that it has an inverse
    2. What is the Range And the Domain of the inverse.

    I really appreciate a good solution so i can learn from my mistakes.
     
  2. jcsd
  3. Oct 31, 2004 #2

    arildno

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    1. Show that F is a strictly increasing function.
    2. The domain of the inverse is the range of F and vice versa.
    3. Welcome to PF!
     
  4. Oct 31, 2004 #3
    so the inverse must be ln(e^x-1)?
     
  5. Oct 31, 2004 #4

    arildno

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    Yeah, that seems right.
     
  6. Oct 31, 2004 #5
    The domain must be then; ]0, infinity[ And the range]-1, Infinity[ or am i wrong?
     
  7. Oct 31, 2004 #6

    arildno

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    Your domain is correct, but the range of the inverse is from negative to positive infinity.
     
  8. Oct 31, 2004 #7
    of course, how stuiped of me :blushing: Thx for the help! :biggrin:
     
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