Let , i.e. deleting ``the line'' only, is there a function such that satisfies and is continuous on this region?
My guess is that such a function would exist, but requires a piecewise definition. A candidate solution I have been working on is . The problem with this solution is having the domain, as I realize it is possible to have , where my solution is well-defined. Is there a way to work around this or should I try something else?