trouble with bijection definition
Hints: First part: Suppose that $f$ is not one-to-one. That implies that $f(x) = f(y)$ for some $x \neq y$. Can $g \circ f$ be a bijection? Similar idea for the other half. Second part: We know that $f$ must be one-to-one and $g$ must be onto. So if $f$ and $g$ are not bijections, then $f$ must not be onto and $g$ must not be one-to-one. See how these two conditions mesh together.