Fuction proof problems

if f(y) is one to one, and f(g(x)) is one to one, is g(x) one to one?
if g(x) is one to one, and f(g(x)) is one to one, is f(y) one to one?
if g(x) and f(g(x)) are onto, is f(y) is also onto?
if f(y) and f(g(x)) are onto, is g(x) is also onto?