# Domain of function

• June 6th 2006, 03:35 PM
starbrite
Algebra question
1/ x^2-10x - 8
I know I have to solve for zero and factor it but when I do it just comes out 1, -5 but the awnser is -1 ,5 ... I just dont understand why ? Sorry math is the subject I struggle with most .Thank you
• June 6th 2006, 03:45 PM
ThePerfectHacker
Quote:

Originally Posted by starbrite
1/ x^2-10x - 8
I know I have to solve for zero and factor it but when I do it just comes out 1, -5 but the awnser is -1 ,5 ... I just dont understand why ? Sorry math is the subject I struggle with most .Thank you

Where is the equation!

$\frac{1}{x^2-10x-8}=??$
• June 6th 2006, 03:48 PM
starbrite
oh sorry its f(x)
I have to find the domain of the function . Thanks
• June 6th 2006, 03:55 PM
ThePerfectHacker
Quote:

Originally Posted by starbrite
oh sorry its f(x)
I have to find the domain of the function . Thanks

It math course they teach you whenever they write a function they always assume all possible values that 'x' can take since you have a fraction,
$\frac{1}{x^2-10x-8}$
It can be any value EXCEPT when the denominator is zero.
Thus,
$x^2-10x-8\not =0$
Since this is not factorable use quadradic formula,
$x=\frac{10\pm \sqrt{100+64}}{2\cdot 1}$
Simplfy,
$x=\frac{10\pm 2\sqrt{41}}{2}$
Thus,
$x=5\pm \sqrt{41}$
---
To make things clearly, let me explain,
$\sqrt{100+64}=\sqrt{164}=\sqrt{4\cdot 41}=2\sqrt{41}$

And, in the final step since the numbers shared a common factor namely 2 I divided it out. Important "you cannot cancel out of a sum" meaning you cannot cancel a 2 with the 10 and leave the other 2. You must to cancel both of them whenever you deal with add/subt.
• June 6th 2006, 04:08 PM
starbrite
oh ok thank u so much