The restriction upon the domain is a result of having a rational function. In this case the part under the radical must be greater than zero.
3-2x>0
-2x>-3
x<3/2
x<1.5
So the domain is all real numbers less than 1.5, or it can be expressed as:
x=(-oo, 1.5) or
-oo<x<1.5