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Math Help - finding domain

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    Exclamation finding domain

    find the domain of the following rational function

    r(x)= 2(x2-6x-40)
    3(x2-100)
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  2. #2
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    Quote Originally Posted by nae33 View Post
    find the domain of the following rational function

    r(x)= 2(x2-6x-40)
    3(x2-100)
    The domain will be all real values of x EXCEPT for the ones that make the denominator equal to zero. Note that there's something interesting about x = 10 that makes it different from x = -10 .....
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    Quote Originally Posted by nae33 View Post
    find the domain of the following rational function

    r(x) = \frac{2\left(x^2 - 6x - 40\right)}{3\left(x^2 - 100\right)}
    Unless otherwise specified, we usually take the domain of a function to be all real numbers for which the function is defined.

    So consider what values of x would make r(x) undefined. Those are the values that are excluded from the domain. (Hint: look for values that would cause things like a division by zero or the taking of the square root/logarithm of a negative number).
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    when i did it i got -10 and 10 as the domain because of the (x2-100)
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    Quote Originally Posted by nae33 View Post
    when i did it i got -10 and 10 as the domain because of the (x2-100)
    Read again the replies you were given. The domain is all real numbers EXCEPT -10 and 10.
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    Quote Originally Posted by nae33 View Post
    when i did it i got -10 and 10 as the domain because of the (x2-100)
    Be careful. The domain is the values for which the function is defined. But when x=\pm10, the function is undefined (due to a division by zero). Thus your answer should be reversed: the domain is all real numbers not equal to \pm10. If you want to write this with set notation, there are several ways:

    \left\{x\in\mathbb{R}\;|\;x\ne10\text{ and }x\ne-10\right\}

    or

    (-\infty,\,-10)\cup(-10,\,10)\cup(10,\,\infty)

    for example.
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  7. #7
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    sorry i ment not = to. i couldnt find the equal sign with the line going through
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