For the functions $f(x)=x+2$ and $g(x)=x^{2}-4,$ find the indicated function and state its domain. Explain the mistake that is made in each problem.
$f(x)-g(x)=x+2-x^{2}-4$
$$
=-x^{2}+x-2
$$
Domain: $(-\infty, \infty)$
This is incorrect. What mistake was made?
