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

thanks.

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.

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

Thanks

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.

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

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.

Thank you for helping now I understand:)