Union of Inverses of Mappings is Inverse of Union of Mappings

Theorem
Let $I$ be an indexing set.

Let $\left\{ { f_i : i \in I } \right\}$ be a family of  mappings.

Then $\left({ \bigcup \left\{ { f_i : i \in I } \right\} }\right)^{-1} = \bigcup \left\{ { f_{i}^{-1} : i \in I } \right\}$

Note
The inverses here are guaranteed only to be relations.