(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Composites of injections/surjections/bijections

**Physics Forums | Science Articles, Homework Help, Discussion**