Suppose the function $g$ and $f$ are one-to-one. Is $f \circ g$ one-to-one?
Suppose $f \circ g$ is one-to-one, are the function $g$ and $f$ one-to-one?
Suppose $f \circ g$ is onto, are the function $g$ and $f$ onto?
Suppose the function $g$ and $f$ are onto. Is $f \circ g$ onto?
I was trying to think of examples to respond to those questions, but I couldn't think of anything.