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Math Help - Undefined functions

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    Undefined functions

    A fraction is undefined if the denominator = 0; obviuosly...

    Are there values that when you take the natural log, the result is undefined?

    Are there values, say x, such that e^x is undefined?

    What are they? Thanks.
    Last edited by jzellt; September 29th 2010 at 07:24 PM. Reason: Mis-spelled word...
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  2. #2
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    Quote Originally Posted by jzellt View Post
    A fraction is undefined if the denominator = 0; obviuosly...

    Are there values that when you take the natural log, the result is undefined?

    Are there values, say x, such that e^x is undefined?

    What are they? Thanks.
    ln(x) and e^x are inverse functions... so the range of the one is the domain of the other.

    Where are you stuck? I think you'll learn more by trying to explain your thoughts than if I just tell you the answers..
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    I just want to make sure I can recognize anytime a function is undefined. I have an exam tomorrow and if I can't recognize this, I won't be able to work out the problems properly...
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    Quote Originally Posted by jzellt View Post
    I just want to make sure I can recognize anytime a function is undefined. I have an exam tomorrow and if I can't recognize this, I won't be able to work out the problems properly...
    I'm afraid that's not a very good excuse. Let's try graphical explanation instead.

    \,e^x

    http://upload.wikimedia.org/wikipedi...px-Exp.svg.png

    \,\log_2(x)

    http://upload.wikimedia.org/wikipedi...rithm_plot.png

    See it?
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  5. #5
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    What you want to know is the domains of those functions- and you should learn that when you learn the functions.

    The domain of ln(x) is "all positive real numbers" and so ln(x) is (literally) undefined for 0 or any negative numbers.

    The domain of e^x is "all real numbers" so e^x is defined for all real numbers.
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