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Math Help - Exponential function requirements

  1. #1
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    Exponential function requirements

    Why do we require that a be a non-negative number in the general expression of an exponential function,

    y = C \cdot a^x \, .

    I understand that a negative value for a would give a very strange function that would fluctuate between negative and positive y-values which in a certain context would make no sense. But I would like to know, purely mathematically speaking, why a has to non-negative.
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  2. #2
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    Re: Exponential function requirements

    What is (-1)^{1/2}?
    Thanks from HallsofIvy
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  3. #3
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    Re: Exponential function requirements

    Quote Originally Posted by emakarov View Post
    What is (-1)^{1/2}?
    I see what you did there. A complex number of course! So [tex]a/tex] must be non-negative because otherwise, for some numbers in the domain, would be mapped to the set of complex numbers?
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