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.