First, look for any restrictions that you know of.
You know that you can not have the logarithm of a nonpositive number, so to start with
Also, since you have a square root, everything under the square root must be nonnegative.
Note that since the denominator is ALWAYS positive, the numerator can not be negative.
So we have in our domain
For both inequalities to hold, .
Thus the domain of f is .