Continuing from the answer of this thread (Link)
"As you notice, for this to work everywhere in the desired domain, we need the domain of $f$ to be (or at least contain) the range of $g$. Thus, the proper definition would have $g:A\rightarrow B$ and $f:B\rightarrow C$ with $f\circ g:A\rightarrow C$."
My question is :
1) In the case above, if we define
$A=\{1, 2\}$
$B=\{r, s, t\}$
$D=\{r, s, u\}$
$C=\{x, y\}$
and
$g:A\rightarrow B$
$f:D\rightarrow C$
image of $g$ $=\{r, s\}$
Will the composition $f\circ g$ still be valid or will it be undefined in this case?