1. ## finding domain

find the domain of the following rational function

r(x)= 2(x2-6x-40)
3(x2-100)

2. Originally Posted by nae33
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 .....

3. Originally Posted by nae33
find the domain of the following rational function

$\displaystyle r(x) = \frac{2\left(x^2 - 6x - 40\right)}{3\left(x^2 - 100\right)}$
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 $\displaystyle x$ 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).

4. when i did it i got -10 and 10 as the domain because of the (x2-100)

5. Originally Posted by nae33
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.

6. Originally Posted by nae33
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 $\displaystyle x=\pm10$, 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.

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