What real numbers are excluded from the domain of the following function?
g(x)=7x+12/x^2+3x+7

Question

What real numbers are excluded from the domain of the following function?
g(x)=7x+12/x^2+3x+7

anonymous · Answer

$$g(x)-\frac{ 7x+12 }{ x^2+3x+7}$$

anonymous · Answer

anything x which makes the denominator zero will be excluded.  you have to solve:$$x^2+3x+7=0$$to find them.

anonymous · Answer

thanks

anonymous · Answer

this one won't factor so use the quadratic formula to get the zeros.

anonymous · Answer

i am right now :)

anonymous · Answer

hint...you're going to run into trouble....

anonymous · Answer

....

anonymous · Answer

what did you get?

anonymous · Answer

can't figure it out! -_- help please?

anonymous · Answer

ok.  the discriminant (the part of the quadratic under the square root sign) will be a negative number.  Since you can't take the square root of a negative number there are no real solutions that make the denominator zero.  i.e, there are no real numbers, x, which make the denominator zero.

anonymous · Answer

so, no matter what real values x takes, this function will accept it :)  The domain is:$$x \in \mathbb{R} $$no real values are excluded.

anonymous · Answer

ok, thanks a lot!

anonymous · Answer

no problem