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Finding the Inverse

  1. Dec 9, 2007 #1
    [SOLVED] finding the Inverse...

    The question asks to find the inverse of

    y = e^(x^(1/4))

    --> I kind of forgot how to proceed for something like this, if anyone can help me, it would be great.
     
  2. jcsd
  3. Dec 9, 2007 #2

    cristo

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    You need to express the function as x(y); that is, make x the subject of the equation.
     
  4. Dec 9, 2007 #3
    I am still not sure...Aren't I supposed to take the ln of both sides or something?
     
  5. Dec 9, 2007 #4

    cristo

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    That would be a good first step, yes.
     
  6. Dec 9, 2007 #5
    ok, ln y = ln e^(x^(1/4))
    = ln y = x^(1/4)
    = ln x = y^(1/4)
    = (ln x)^4
    ...easy now lol.
     
  7. Dec 10, 2007 #6
    I would suggest to check this again...
     
  8. Dec 10, 2007 #7

    HallsofIvy

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    Assuming he has already checked it, why "again"?

    If f(x)= [tex]e^{x^{1/4}}[/itex] then [itex]f^{-1}(x)= (ln(x))^{4}[/itex]

    For all positive x.

    [tex]f(f^{-1}(x))= e^{(ln(x))^4)^{1/4}}= e^{ln(x)}= x[/tex]
    [tex]f^{-1}(f(x))= (ln(e^{x^{1/4}}))^4= (x^{1/4})^4= x[/tex]

    Looks good to me. Of course, both functions have domain and range "all positive numbers".
     
  9. Dec 10, 2007 #8
    All right, I see the intention of the original post. The inverse was calculated as:
    [tex]x=f^{-1}(y)[/tex]
    and the symbols were switched. My mistake, sorry.
     
  10. Dec 10, 2007 #9
    y = e^(x^(1/4))

    x = e^(y^(1/4))
    ln^x = y^1/4
    y = (ln^x)^4

    i guess you got it.. lol, i took a few seconds of my surfing time to solve it when you already got it.
     
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