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Math Help - how to find the Domain definition of Function

  1. #1
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    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.
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  2. #2
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    Factorise the denominator. The function will be continuous everywhere except where the denominator is 0.
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  3. #3
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    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.
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  4. #4
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    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).
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  5. #5
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    thank you.

    and yes i mean How do I factor.
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