# how to find the Domain definition of Function

• Dec 8th 2010, 01:56 AM
ZOOZ
how to find the Domain definition of Function
you can see the Function in the picture.

what is the way to find the Domain definition ?

thanks.
• Dec 8th 2010, 02:04 AM
Prove It
Factorise the denominator. The function will be continuous everywhere except where the denominator is 0.
• Dec 12th 2010, 01:29 AM
ZOOZ
YES i know if there 0 in the Denominator so the Factorise are not continuous but Can have more points in the denominator to compare it to zero .

how i find Them?

thanks.
• Dec 12th 2010, 02:07 AM
HallsofIvy
So your question really is "How do I factor \$\displaystyle x^4- 3x^3+ 9x^2- 7x\$?" It would have been better to say that in your first post.

"x" is an obvious factor: \$\displaystyle x^4- 3x^3+ 9x^2- 7x= x(x^3- 3x^2+ 9x- 7)\$. Now the only possible zeros of \$\displaystyle x^3- 3x^2+ 9x- 7\$ are 1, -1, 7, and -7 (because if it were to factor as (x-a)(x-b)(x-c) the last term would be abc=-7- and the only integer factors of 7 are 1 and 7). Trying x= 1 in the polynomial we get \$\displaystyle 1^3- 3(1^2)+ 9(1)- 7= 1- 3+ 9- 7= 0\$. That tells us that x- 1 is also a factor. Dividing \$\displaystyle x^3- 3x^2+ 9x- 7\$ by x- 1 leaves \$\displaystyle x^2- 2x+ 7\$ which has discriminant (\$\displaystyle b^2- 4ac\$) equal to \$\displaystyle (-2)^2- 4(1)(7)= 4- 28= -24\$ so there are no more real number zeros of the polynomial. \$\displaystyle x^4- 3x^3+ 9x^2- 7x= x(x-1)(x^2- 2x+ 7)\$.
• Dec 12th 2010, 05:56 AM
ZOOZ
thank you.

and yes i mean How do I factor.