For Any Function $f : A \rightarrow B$ , Define a New Function

Short Answer

For any function $f : A \rightarrow B$ , define a new function $g : \mathcal { P } ( A ) \rightarrow \mathcal { P } ( B )$ as follows : for every $S \subseteq A , g ( S )$ = $\{ f ( x ) \mid x \in S \}$ Prove that $f$ is onto if and only if $q$ is onto.