Image of Composite Mapping

Theorem
Let $f: S \to T$ and $g: R \to S$ be mappings.

Then:


 * $\operatorname{Im} \left({f \circ g}\right) = f \left({\operatorname{Im} \left({g}\right)}\right)$

where $f \circ g$ is the composition of $g$ and $f$, $\operatorname{Im}$ denotes image, and the $f$ signifies taking image of a subset under $f$.

Also see

 * Image and Preimage of Composition of Relations