# Thread: how to find the Domain definition of Function

1. ## 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.

2. Factorise the denominator. The function will be continuous everywhere except where the denominator is 0.

3. 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.

4. So your question really is "How do I factor $x^4- 3x^3+ 9x^2- 7x$?" It would have been better to say that in your first post.

"x" is an obvious factor: $x^4- 3x^3+ 9x^2- 7x= x(x^3- 3x^2+ 9x- 7)$. Now the only possible zeros of $x^3- 3x^2+ 9x- 7$ 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 $1^3- 3(1^2)+ 9(1)- 7= 1- 3+ 9- 7= 0$. That tells us that x- 1 is also a factor. Dividing $x^3- 3x^2+ 9x- 7$ by x- 1 leaves $x^2- 2x+ 7$ which has discriminant ( $b^2- 4ac$) equal to $(-2)^2- 4(1)(7)= 4- 28= -24$ so there are no more real number zeros of the polynomial. $x^4- 3x^3+ 9x^2- 7x= x(x-1)(x^2- 2x+ 7)$.

5. thank you.

and yes i mean How do I factor.