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

a) Prove or disprove: If f:X---->Yhas at least one left inverse g:Y---->X but has no right inverse, then f has more than one such left inverse.

b) Prove or disprove: If f and g are maps from a set X to X and fog is injective, then f an g are both injective. (fog being function composition).

2. Relevant equations

3. The attempt at a solution

a) I think it is true.

Assume f only has one such inverse, i.e. g is unique.

If f has no right inverse, there exists no map h such that f(h(a))=a for all a in X.

g(f(a))=a for all a in X.

b) False, found a counterexample. the inner function need not be injective. Still stuck on a though.

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# Homework Help: Left and right inverses

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