Find range of values

• Nov 1st 2009, 08:21 PM
arze
Find range of values
find the range of values for k for which the function
$\displaystyle \frac{x^2-1}{(x-2)(x+k)}$
where x is real, takes all real values.
I don't know how to start. Any pointers?
Thanks
• Nov 4th 2009, 11:30 AM
statmajor
The question asks you for what values of X, would F(x) exist. Or what values of X would F(x) not exist.

Hint: C/0 doesn't exist (where C is an arbitrary constant).
• Nov 4th 2009, 03:55 PM
arze
so x cannot be 2 or -k. i dont know what else the answer is $\displaystyle |k|\leq 1$
• Nov 4th 2009, 04:10 PM
statmajor
Sorry, I misread the question. I thought you were supposed to find values for x instead of k.

So same as idea as before. We know that k cannot be -x and we also know that x can't be 2. Therefore, k cannot be -2 (I think).
• Nov 4th 2009, 06:29 PM
arze
ok got that, but how to continue confuses me :(
• Nov 4th 2009, 07:00 PM
statmajor
What part are you confused about? You know that k can't be -x, and when x = 2, k can't be -2.
• Nov 4th 2009, 07:01 PM
arze
yes, i meant how to find the values of k other than that it isn't -2.
• Nov 4th 2009, 07:19 PM
statmajor
The domain for is k $\displaystyle (- \infty, -x)\cup(-x, \infty)$
The domain of x is $\displaystyle (- \infty, -2)\cup(-2, \infty)$