0 votes 0 votes If $f$ and $fog$ are onto, does it follow that $g$ is onto?Justify your answer. Set Theory & Algebra kenneth-rosen discrete-mathematics set-theory&algebra difficult + – Pooja Khatri asked Apr 9, 2019 Pooja Khatri 360 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Suppose that g ◦ f is surjective. Let z ∈ C. Then since g ◦ f is surjective, there exists x ∈ A such that (g ◦ f)(x) = g(f(x)) = z. Therefore if we let y = f(x) ∈ B, then g(y) = z. Thus g is surjective. Vishal_kumar98 answered Sep 30, 2021 Vishal_kumar98 comment Share Follow See all 0 reply Please log in or register to add a comment.