Suppose we have a function $f:X \rightarrow Y$. Now, consider the function $g:X'\rightarrow Y$ where $X'\subset X$.
I'd like to say the $g$ is a "subset" of $f$ ; is there a correct term for describing $g$ w.r.t $f$?
NB: Also, $g(x) = f(x)$ for $x \in X'$