If $g$ is one-to-one and $f$ is onto, then we can't say anything about $f \circ g$, correct?
and if $f\circ g$ is one-to-one and onto, then $g$ is one-to-one and $f$ is onto?
$g(x) > f(g(x)) = f \circ g$
$A > Z$ and $Z > B$
we need to look at set $A$ (all elements of $A$ have to map to one unique element of $Z$ to see whether a function $g$ is one-to-one and set $B$ to see if $f$ is onto (there's an arrow to every elements).
Just wanted to make sure I understood correctly.