I think what you want is: \mathbb{R}

Anyway, let's calculate . Note that is undefined, so can only be a continuous function of .

Note: The final simplification is only possible if . If , then is a constant function and obviously continuous. Similarly, if , you also have a constant function, which is obviously continuous. So, assume and .

Since , the function is odd. So, you only need to consider continuity for and by symmetry, you will find continuity for all .

Now, given , , and , you want to find that works. First of all, we are going to want to limit the possible range of . We know that the function is not continuous at , so .

Does this help at all?