I did this:
-but, is there a more 'technical' way of computing this rather than using the definition of both absolute value and inverses such as in the following.
If you're only interested in an inverse relation, not a function, then I would agree that the situations are analogous. Incidentally, you should write the inverse as the following:
The graph of the inverse relation is merely the original graph flipped about the line , as indeed, all inverse relations in 2 dimensions are produced in the same way.