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Math Help - Functions and their domains

  1. #1
    Member
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    Functions and their domains

    I was looking over my notes recently, and this kind of problem was written
    f(x)=\sqrt{5-3x}

    The domain is defined for all values of x<(inclusive) \frac{5}{3}, right?

    then I have something weird written for function
    \frac{1}{\sqrt{5-3x}}


    the domain is defined for x belongs to ]-\infty,\frac{5}{3}]\cup x belongs to [\frac {5}{3},\infty[



    This can't be right?


    I clearly rememver myself saying that the answer is x is greater than 5 over three, and the teacher said it was correct.
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  2. #2
    Junior Member
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    Jun 2007
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    Yes it is  x \le \frac{5}{3}

    This is because nothing in the radical can be negative so 0 has to be the lowest we can go, so \frac{5}{3} is the lowest you can go before going into imaginary numbers, which cannot be graphed on the real plane.

    For the second one you have written x cannot be 0 so the domain would be  x < \frac{5}{3}
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