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Math Help - Classifying Function

  1. #1
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    Classifying Function

    Let f(x)=x^{x}.

    Is f(x) a power function, exponential function, both or neither?
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  2. #2
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    It is a power-exponential function.
    That means it has higher order than an exponential function (it grows "faster" than an exponential).
    Iīm not quite sure if thatīs how you say it in english, in highschool it was called "potencial-exponencial", an I tried to translate it as closely as possible.
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  3. #3
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    So it's both? I don't completely understand why it should be both and not neither though; I wouldn't know how to explain this. I've never heard of this type of function before and I wouldn't know how to justify any of them.

    Thanks a lot for your help!
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  4. #4
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    Is this answer correct?

    The function f(x)=x^x is neither a power function nor an exponential function. A power function has the independent variable as the root being raised to a fixed power, and an exponential function has a fixed number root being raised to the independent variable. By having the independent variable as the root and the exponent, the function is neither a power function nor an exponential function.
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