Why If $f: A \rightarrow B$ is an $R$- module homomorphism then $f(T(A)) \subset T(B)$?

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Why If $f: A \rightarrow B$ is an $R$- module homomorphism then $f(T(A)) \subset T(B)$?, where $T(A)$ is called the torsion submodule.

Could anyone clarify this for me please?