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pop000 · Dec 11, 2010, 07:47 AM

I need to find the Domain definition of this Function:1/x^4-3x^3+9x^2-7

thanks.

galactus · Dec 11, 2010, 10:06 AM

You have written:

$\frac{1}{x^{4}}-3x^{3}+9x^{2}-7$ .

I assume you mean:

$\frac{1}{x^{4}-3x^{3}+9x^{2}-7}$

This is why grouping symbols are important.

pop000 · Dec 11, 2010, 11:10 AM

Yes this what I mean so how I find the Domain definition?

Thanks

galactus · Dec 11, 2010, 11:21 AM

Which one? You did not say. I assume that latter? Does find the 'Domain definition' mean find the domain?

If so:

Factor the denominator. Set the factors equal to 0 and solve for x.

These are the values NOT in the domain because they result in division

by 0.

This particular quartic has 2 real and 2 complex roots. I assume you are

not dealing with the complex so find the two real roots.

Graph it and you can see the vertical asymptotes. That is where there is

division by 0 and not in the domain.

pop000 · Dec 12, 2010, 01:46 AM

I mean the second Equation but is not 7 is need to be 7x

galactus · Dec 12, 2010, 01:58 AM

Is this correct?:

$\frac{1}{x^{4}-3x^{3}+9x^{2}-7x}$

If so, factor:

$\frac{1}{x(x-1)(x^{2}-2x+7)}$

Set each factor to 0. x=0 is one solution, x=1 is another.
The remaining quadratic has complex roots.

The values x=0 and x=1 are NOT in the domain because they give division by 0.

pop000 · Dec 12, 2010, 07:44 AM

Thank you for helping now I understand:)