SOLUTION: what are the values of x that are not in the domain of the expression where f(x) equals the numerator of x-3 and the denominator of x^2+14x+48

The domain is the entire number line except two points, two real numbers that are 

the roots of the quadratic polynomial x^2 + 14x + 48 in the denominator.



In other words, the domain is entire number line except two points, two real numbers that make the denominator equal to ZERO.


How to find these points ?


Solve the equation x^2 + 14x + 48 = 0.


To solve it, factor the left side

(x + 6)*(x + 8) = 0.


Then you see that the roots are x= -6  and x= -8.


So, you answer is:

The domain is all the set of real numbers except x= -6 and x= -8, where the denominator becomes equal to ZERO.