the domain rational function of R(x)=-7-4x/x^3-6x^2-7x

Question

What's the result of this and how do I get answer

Answer 1

Domain is the set of x values in which the function is defined. To find the domain, set the denominator equal to zero.  This is because the denominator cannot be equal to zero.  By solving for x from doing this, we can find all the restrictions.

 

 

x³ - 6x² - 7x = 0

 

 

Factor out an x.

 

x(x² - 6x - 7) = 0

 

 

We can factor completely.

 

x(x + 1)(x - 7) = 0

 

 

Set the factors equal to zero.

 

x = 0            x + 1 = 0            x - 7 = 0

 

                    x = -1                 x = 7

 

 

The domain is all real numbers except for -1, 0, and 7.

Answer 2

For a rational function R(x) = P(x) / Q(x) where P and Q are polynomials, the only restrictions on the domain are that the denominator cannot equal 0  

 

So set Q(x) = 0 to find the restricted values  

 

The domain will be all real numbers except the restricted values  

 

If you need help finding where Q(x) = 0 comment back or repost the question specifically asking for that