All real numbers except -.5 and 0.
Work Step by Step
Once again, $g$ has a domain restriction that it cannot be $0$, for it has $x$ in the denominator of a fraction. However, since we are dividing by $h$, it is also in the denominator of the fraction and cannot be 0. Thus, we see that the function also does not exist when $x$ equals -.5. Thus, the domain is all real numbers except -.5 and 0.