There is an easy way to determine the domain of a function.  If the denominator is 1 and there are no radicals in the numerator, the domain is all real numbers.

If there is a variable in the denominator and no radical in the denominator, the domain is all real numbers except the value of x that will give a zero in the denominator.

If there is a radical with an even root, square root, fourth root, etc.  You have to solve for x such that the value under the radical is greater than or equal to zero. The domain is all real numbers except for that value.

If there is a radical with an odd root, then the domain is all real numbers.