Preimage of Subset under Mapping/Examples/Preimages of f(x, y) = x y

Example of Preimage of Subset under Mapping

 * Reciprocal-function.png

Let $f: \R^2 \to \R$ be the real function of $2$ variables defined as:
 * $\forall \tuple {x, y} \in \R^2: \map f {x, y} = x y$

Let the following subsets of $\R^2$ be defined:

Then: