Domain of f(x)=x^2+7x+12/x^2+11x+28

Question

I just need help with this question, it's difficult and I don't understand it. 

Answer 1

The domain of the function is all real x, except for where the denominator equals zero. In order to determine where this denominator equals zero, you may factor x² + 11x + 28 to find the roots. Can you handle it from here?

Answer 2

You cannot divide any number by zero, it is undefined in math. Therefore your domain (x-values you select) cannot cause the denominator to equal zero. To determine those x-values factor the denominator:

 

 Denominator:  x^2 + 11x + 28

 

This will factor to:

 

(x+4) (x+7) set this equal to zero to find the x-values of the roots.

 

(x+4) (x+7) = 0 this implies x=-4 or x=-7

 

Answer: Domain is all real x-values except -4 and -7.