This problem is really more a test of understanding the definitions of "domain" and "range". The domain of a function are the legal values one can put into the function and one typically is looking for radicals [can't take a negative square root] or fractions [can't divide by zero] to determine the domain of a function. The range of a function is the set of all values a function is able to produce.

These problems can best be approached through Algebrator's Function Wizards.  To help you clearly understand our desktop software and how appropriate it may be for your needs, please use one of the following links to obtain a free trial of the program:

Windows: http://www.softmath.com/tr/alg51win-tr-en.exe

Mac: http://www.softmath.com/tr/alg51mac-tr-en.dmg

Using doyourmath.com, however, look for valid numbers for "the square root of 6x-3", solve "6x-3>=0".  Solving the equation "y=sqrt(6x-3)" shows which legal values are for range. 

https://doyourmath.com/redirect/174/3f55d74973c0ac77c742ad7033610d42?q=c%3Dsolve_solveproblem%26v1%3Dy%253D%5Csqrt%7B6x-3%7D%26v2%3Dsolve%26v3%3Dx%3C%2Fp%3E

So the domain is examined by solving "6x-3>=0". 

https://doyourmath.com/redirect/174/3f55d74973c0ac77c742ad7033610d42?q=c%3Dsolve_solveproblem%26v1%3D6x-3%253E%253D0%26v2%3Dgraph%3C%2Fp%3E

So it demonstrates that the domain is "x>=(1/2)".