find the domain of the following rational function

r(x)=2(x2-6x-40)

3(x2-100)

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- Jul 7th 2008, 05:55 PMnae33finding domain
find the domain of the following rational function

r(x)=__2(x2-6x-40)__

3(x2-100) - Jul 7th 2008, 06:05 PMmr fantastic
- Jul 7th 2008, 06:05 PMReckoner
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 $\displaystyle x$ would make $\displaystyle r(x)$ 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). - Jul 7th 2008, 06:09 PMnae33
when i did it i got -10 and 10 as the domain because of the (x2-100)(Worried)

- Jul 7th 2008, 06:13 PMmr fantastic
- Jul 7th 2008, 06:14 PMReckoner
Be careful. The domain is the values for which the function

*is*defined. But when $\displaystyle x=\pm10$, 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 $\displaystyle \pm10$. If you want to write this with set notation, there are several ways:

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

or

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

for example. - Jul 7th 2008, 06:23 PMnae33
sorry i ment not = to. i couldnt find the equal sign with the line going through