You don't need to calculate it for the first square root. If you need a justification you can start by looking at . This is a parabola centered at the origin and it opens to the right (towards positive x-values). So x can only have positive values. This is equivalent to . In your case you are taking the positive square root, which will be the part of the parabola above the x-axis, that is the square root evaluates to only value greater or equal to 0.
In your first case, the range is . In the second expression you are taking the reciprocal of the first function. The range is . Here is how you get it. Lets look at a point in the first range. To get the range of the second one, we take the reciprocal, i.e. . When y is close to 0 we get a big number, so on one side the range can be arbitrarily large. However, if we make really large, we are making really tiny, so the range is 0 at the other end. The range ought to be , but since you can never make zero, it must be an open interval -