The domain for this function is restricted because you may not divide by zero. All real values of x except those that create division by zero situations are legal. The offending values of x are -2 and 0, so that is why the domain is as you have stated.
1. Find the domain of the function.
$\displaystyle g(x) = 1/x - 3/(x+2)$
I know the answer is $\displaystyle (- \infty,-2) \ \ or \ \ (-2,0) \ \ or \ \ (0, +\infty)$
but why?
Because x cannot equal 0, and x cannot equal -2. Everything else is ok.