find the range of values forkfor which the function

$\displaystyle \frac{x^2-1}{(x-2)(x+k)}$

wherexis real, takes all real values.

I don't know how to start. Any pointers?

Thanks

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- Nov 1st 2009, 08:21 PMarzeFind 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 AMstatmajor
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 PMarze
so x cannot be 2 or -k. i dont know what else the answer is $\displaystyle |k|\leq 1$

- Nov 4th 2009, 04:10 PMstatmajor
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 PMarze
ok got that, but how to continue confuses me :(

- Nov 4th 2009, 07:00 PMstatmajor
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 PMarze
yes, i meant how to find the values of k other than that it isn't -2.

- Nov 4th 2009, 07:19 PMstatmajor
The domain for is k $\displaystyle (- \infty, -x)\cup(-x, \infty)$

The domain of x is $\displaystyle (- \infty, -2)\cup(-2, \infty)$