1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inverse Functions

  1. Oct 7, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the inverse:

    y = (e^x)/(e^x + 1)

    2. Relevant equations



    3. The attempt at a solution

    I switched x with y and solved for y but I ended up getting lne^y - lnx = lne^y +ln1 and then -lnx= ln1
     
  2. jcsd
  3. Oct 7, 2007 #2
    could you show your work?

    and I think you split up e^x+1 to lne^y+ln1? you can't do that.
     
  4. Oct 7, 2007 #3
    ohhh your right it should be

    e^y = x(e^y+1)

    then

    lne^y = lnx + ln(e^y+1) but i'm still stuck from here
     
  5. Oct 7, 2007 #4
    hm..ok take the ln(e^y+1) to the right side and simplify by combining the ln's

    edit: whops meant take lne^y to the right side, lnx to the left and you should be able to simplify it
     
  6. Oct 7, 2007 #5
    what is there to combine
     
  7. Oct 7, 2007 #6
    so get -lnx = ln(e^y + 1) - lne^y

    then -lnx = ln((e^ y +1)/e^y) ? this doesn't seem like it helped now im back to where i started.
     
  8. Oct 7, 2007 #7
    hm..no I multiplied by -1 on the RHS and LHS and got x=-lny but plugging that in I get y=1+y >.<
     
  9. Oct 7, 2007 #8
    could you show the steps I'm not seeing it
     
  10. Oct 7, 2007 #9
    wow did that wrong too >.>

    my algebra is really bad right now for some reason...hm..try multiplying/dividing by [tex]\frac{e^{-x}}{e^{-x}}[/tex]

    ok yes multiply/divide by that and you will find the inverse.
     
    Last edited: Oct 7, 2007
  11. Oct 7, 2007 #10
    so do that by the original equation before i start trying to find the inverse ?
     
  12. Oct 7, 2007 #11
    i got -ln(1/x -1) = y for the inverse would anyone agree ?
     
  13. Oct 7, 2007 #12
    yes and try to get x^-x all by itself on the RHS or LHS so you don't have something like ln(e^x+1)=y
     
  14. Oct 7, 2007 #13
    yep that's what I got, and you can check by plugging it in. also should be x=f(y).
     
  15. Oct 7, 2007 #14
    gotcha :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Inverse Functions
  1. Inverse of a function (Replies: 0)

  2. Inverse of a function (Replies: 2)

  3. Inverse functions (Replies: 5)

  4. Inverse of a function (Replies: 2)

  5. Inverse Functions (Replies: 19)

Loading...