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Math Help - Domain for x^a

  1. #1
    Senior Member Twig's Avatar
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    Domain for x^a

    For the function f(x)=5x^{\frac{2}{5}} e^{x} , what is the domain of this function?

    Mathematica and Matlab says it is only x\geq 0 .

    But our math teacher did a solution where she looked for the stationary points of f(x) . She answered that x=- \frac{2}{5} was a stationary point. But this value is negative!

    She claimed that the domain of f(x) was \mathbb{R} .
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  2. #2
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    Does  (-1)^{2/5} have a real solution? (I honestly don't know, I REALLY need to read up on my exponents with negative bases), but if a real solution exists for that, then indeed the domain is R.

    If only complex solutions exist, the domain is the set of x values such that x is greater than or equal to 0 (assuming the function you're working with maps only to R).
    Last edited by JG89; August 19th 2009 at 09:19 AM.
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  3. #3
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    Well why not? :-/

    Take any negative number,
    say -32.

    Now (-32)^2/5 is the same as {(-32)^1/5}^2
    So basically what we have is 4.

    in other words, x^2/5 is merely the square of the fifth root of x. Now the fifth root exists for negative reals as well.

    Law of indices. {(a)^b}^c = (a)^(bc)
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Your instructor is correct


    (-1)^2/5 = 1

    x^(m/n) is defined for all x if n is odd
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