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Inverse Function

  1. Oct 14, 2007 #1
    Question:
    If g(x) = 5 + x + e^x, find g^-1(6) [inverse of g, not g to the power of -1]

    Attempted:
    So I first substitued g(x) to y

    So y = 5 + x + e^x
    then I tried isolating the x
    So y - 5 = x + e^x
    Then I applied ln to both sides
    ln(y) - ln(5) = ln(x) + ln(e^x)
    Due to the log rules, I can take down the x from ln(e^x)
    So it becomes ln(y) - ln(5) = ln(x) + x(ln(e))
    And since ln(e) = 1, that means
    ln(y) - ln(5) = ln(x) + x

    Ok. So now I'm stuck.
    Where should I go from here?? I know I'm missing something extremely crucial here, but I'm really not seeing it :(
    Please help! And thanks a bunch!!
     
  2. jcsd
  3. Oct 14, 2007 #2

    dt_

    User Avatar

    You applied the ln incorrectly. You'd be getting ln (y-5), not ln y - ln 5.

    See if you can go from there :smile:

    Anyway, the idea for finding an inverse function like this is, replace all the y with x, and replace all the x with y. Then solve for the new y, which is the inverse function. Then plug in the given x.
     
  4. Oct 14, 2007 #3
    Oh, really? XD
    So if it's ln(y - 5) then x and e^x would be ln(x + e^x) right?
    I.. don't know where to go from there.. :(
     
  5. Oct 14, 2007 #4

    Gib Z

    User Avatar
    Homework Helper

    You could think of the question as saying: What value of x would make [tex]5+x+e^x=6[/tex]?

    In other words, find x, if [tex]x+e^x = 1[/tex].

    Now, you can either take the log of both sides here, but really its just easy to see that its 0.
     
  6. Oct 14, 2007 #5
    Oh wow.. so I was making this question harder than it seems XD
    Thanks so much, Gib Z!! :D
    Brownie points for you :D :D
     
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