Did you graph these two functiona?
That will tell you a great deal.
Range: It is all real such that the equation has a solution for in the domain. Thus, it means we want to solve, and RHS is always non-negative thus LHS must be non-negative and so we have a constraint that . Square both sides, since a square root exists and so the solution is but we want that . If then which is always true. And similarly with . Thus, the range is .