Preimage of Subset under Mapping/Examples/Preimage of 0 under x^2-x-2

Example of Preimage of Subset under Mapping
Let $f: \R \to \R$ be the mapping defined as:


 * $\forall x \in \R: \map f x = x^2 - x - 2$

The preimage of the singleton $\set 0$ is:


 * $f^{-1} \sqbrk {\set 0} = \set {-1, 2}$

which is the set of roots of $f$.

Proof
Hence the result.