Find the domain of f (x) = 1 / squareroot of 3-2x.

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