If $f \circ g$ is onto then $f$ is onto and if $f \circ g$ is one-to-one then $g$ is one-to-one
This post intends to remove this question from the Unanswered list.
As noted in the comments, all of your assertions are correct.
If $f \circ g$ is onto then $f$ is onto and if $f \circ g$ is one-to-one then $g$ is one-to-one
This post intends to remove this question from the Unanswered list.
As noted in the comments, all of your assertions are correct.