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Math Help - Inverses

  1. #1
    Member akhayoon's Avatar
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    Inverses

    Is the inverse of  f(x)=ln|x|~if x<0 if it's g lets say

    g(x)=e^{|x|}??

    if so is the domain all real numbers (for the inverse I mean)?

    then the question says find a formula for computing g(y) for each y in the domain of g
    Last edited by akhayoon; December 9th 2007 at 07:11 AM. Reason: typo
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  2. #2
    Member akhayoon's Avatar
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    is e^{|x|} some kind of parabola or something too?
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    GAMMA Mathematics
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    Quote Originally Posted by akhayoon View Post
    is e^{|x|} some kind of parabola or something too?
    Actually, yes it is because the negative side should mirror the positive side with f(0)=1.
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    Quote Originally Posted by akhayoon View Post
    Is the inverse of  f(x)=ln|x|~if x<0 if it's g lets say

    g(x)=e^{|x|}??

    if so is the domain all real numbers (for the inverse I mean)?

    then the question says find a formula for computing g(y) for each y in the domain of g
    You already have the second part:
    g(y) = e^{|y|}

    Quote Originally Posted by akhayoon View Post
    is e^{|x|} some kind of parabola or something too?
    It does look a bit "parabola-ish" doesn't it? (However it has little relation to an actual parabola.) We say that the function g(x) = e^{|x|} has "even symmetry" when g(-x) = g(x) as this one does.

    -Dan
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  5. #5
    GAMMA Mathematics
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    It does look a bit "parabola-ish" doesn't it? (However it has little relation to an actual parabola.) We say that the function has "even symmetry" when as this one does.
    Yes, to be clear you shouldn't call it a parabola, but just state the fact that it is an even function. It probably doesn't matter unless you are in an Analysis class.
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    Quote Originally Posted by akhayoon View Post
    Is the inverse of  f(x)=ln|x|~if x<0 if it's g lets say

    g(x)=e^{|x|}??

    if so is the domain all real numbers (for the inverse I mean)?

    then the question says find a formula for computing g(y) for each y in the domain of g
    The inverse of y=ln|x|=ln(-x) (x<0) is y=-e^x.
    Attached Thumbnails Attached Thumbnails Inverses-lnx-its-inverse.gif  
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  7. #7
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    As you can see, the inverse (like all functions that have inverses) is mirrored across the line y=x of the original function.
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