Find range of values

**arze** · November 1st 2009, 08:21 PM

find the range of values for k for which the function
$\frac{x^2-1}{(x-2)(x+k)}$
where x is real, takes all real values.
I don't know how to start. Any pointers?
Thanks

**statmajor** · November 4th 2009, 11:30 AM

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).

**arze** · November 4th 2009, 03:55 PM

so x cannot be 2 or -k. i dont know what else the answer is $|k|\leq 1$

**statmajor** · November 4th 2009, 04:10 PM

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).

**arze** · November 4th 2009, 06:29 PM

ok got that, but how to continue confuses me

**statmajor** · November 4th 2009, 07:00 PM

What part are you confused about? You know that k can't be -x, and when x = 2, k can't be -2.

**arze** · November 4th 2009, 07:01 PM

yes, i meant how to find the values of k other than that it isn't -2.

**statmajor** · November 4th 2009, 07:19 PM

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

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