the domains here will be pretty much the same as if z was a real number.

Hint: when the domain is not restricted, polynomials are onto the whole complex plane (consequence of the Fundamental theorem of Algebra)Describe the range of each function:

g. f(z)=z+5 for Re z>0

h. g(z)=z^2 for z in the first quadrant, Re z >=0, Im z >=0

consider, regarding the range: what happens when z approaches zero? what happens if it is on the unit disk?

i. h(z)= 1/z for 0<|z|<=1

see my comment for (g) and (h)j. p(z)=-2z^3 for z in the quarter-disk |z| < 1, 0<Arg z<pi/2

now, what can you come up with?