How do I find the domain and (if any) discontinuities for g(x)=(x^2+6x+9)/(x+3)? I don’t entirely understand what is being asked by domain and discontinuity.
1 Answer
The domain of
It has a hole (removable singularity) at
Explanation:
Given:
g(x) = (x^2+6x+9)/(x+3)
Note that when
If we factor the numerator, we find:
x^2+6x+9 = (x+3)(x+3)
So:
g(x) = (x^2+6x+9)/(x+3) = (color(red)(cancel(color(black)((x+3))))(x+3))/color(red)(cancel(color(black)((x+3)))) = x+3
with exclusion
Note that the simplified expression for
So