Discrete Math composition functions Give examples of sets $X$, $Y$, $Z$ and functions $f: X \to Y$, $g: Y \to Z$, so that
the composition $g\circ f: X \to Z$ is a bijection, although neither $f$ or $g$ it is.
I have no idea to begin thinking on amounts.

WLOG we can take $Z = X$ and $g \circ f = Id$ 
If you can apply $f$ without "losing information", it's because $f$ is bijective on its image, i.e. injective.
Thus take Y bigger than X.
Then you just have to left invert $f$.
If you want to take $Z \neq X$ and $g \circ f \neq Id$, just left compose with a bijection from $X$ to $Z$.
