(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider arbitrary sets A, B, C and D with arbitrary functions:

f:A-->B, g:B-->C, h:C-->D. We define a composite function

h o g o f:A-->D.

Given that h, f, and h o g o f are bijective, and g is injective, show that g is also surjective (i.e. g is bijective).

This seems almost trivial to me, but my TA says that it requires proving.

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# Composites of injections/surjections/bijections

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