Editing Bijection (section)

==Composition==
[[Image:Bijective composition.svg|thumb|300px|A bijection composed of an injection (X → Y) and a surjection (Y → Z).]]

The [[Function composition|composition]] <math>g \,\circ\, f</math> of two bijections ''f'': ''X → Y'' and ''g'': ''Y → Z'' is a bijection, whose inverse is given by <math>g \,\circ\, f</math> is <math>(g \,\circ\, f)^{-1} \;=\; (f^{-1}) \,\circ\, (g^{-1})</math>.

Conversely, if the composition <math>g \, \circ\, f</math> of two functions is bijective, it only follows that ''f'' is [[Injective function|injective]] and ''g'' is [[surjective function|surjective]].