Suppose that $f:A \longrightarrow B$ and $g:B \longrightarrow C$ are functions.
If $g \circ f$ is onto and $g$ is one-to-one, then prove that $f$ is onto.
How do I go about proving this?
From $g \circ f$ is onto, I know that there exists an $a \in A$ such that $g(f(a))=c$ and I also know that if $g(b_1)=g(b_2)$ then $b_1=b_2$ from the definition of one-to-one, but I'm not sure where to go from there. Any help would be great :)