Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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 :)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook