what is the domain of f(x)=-z^2-4z+7
Your notation is not correct. (I don't think)
f(x)=-z^2-4z+7
you have f(x) but then you have used z not x so it doesn't make sense.
however, if you mean
f(x)=-x^2-4x+7
then this is a concave down parabola.
The domain is all real x.