Question 1083440
The domain is all the values x may take on. g(x)=-x^2 has a domain of all real numbers, for x may take on any number.  When there are radicals, the domain can't make the value under the radical negative.  If there is a fraction, the denominator cannot be 0.

The range is all the values y may have.  Here, since x^2 is always 0 or positive, the range is 0 to negative infinity.  One can graph equations to get an idea, but often one has to put in values of x and see what y is.