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Math Help - Inverse f(x)

  1. #1
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    Inverse f(x)

    Well. I have to figure out the inverse function of a particular function.

    That function being ln|x-2| + 3.

    I got it to x-3 = ln|y-2|, but how do I get y on it's own? I imagine it has some to do with e^x considering it's ln|x|'s inverse.

    Well I think I've got it now to be e^(x-3) + 2
    Last edited by StephenPoco; March 8th 2010 at 09:12 AM.
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  2. #2
    Member Miss's Avatar
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    Quote Originally Posted by StephenPoco View Post
    Well. I have to figure out the inverse function of a particular function.

    That function being ln|x-2| + 3.

    I got it to x-3 = ln|y-2|, but how do I get y on it's own? I imagine it has some to do with e^x considering it's ln|x|'s inverse.

    Well I think I've got it now to be e^(x-3) + 2
    Are you sure you not given an interval in the question?
    This function is not one-to-one function.
    Last edited by Miss; March 8th 2010 at 11:31 AM.
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  3. #3
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    Quote Originally Posted by StephenPoco View Post
    Well. I have to figure out the inverse function of a particular function.

    That function being ln|x-2| + 3.

    I got it to x-3 = ln|y-2|, but how do I get y on it's own? I imagine it has some to do with e^x considering it's ln|x|'s inverse.

    Well I think I've got it now to be e^(x-3) + 2 and x > 2
    That's only half of the truth ...

    1. I assume that the function is

    f(x)=\left\{\begin{array}{rcl}\ln(x-2)+3&~if~&x>2 \\ \ln(2-x)+3&~if~&x<2 \end{array}\right.

    2. Each "branch" of f is a one-to-one function. Therefore you have to calculate 2 different inverses.
    Attached Thumbnails Attached Thumbnails Inverse f(x)-invers_lnfkt.png  
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