1. The problem statement, all variables and given/known data If f :X -> X and g:X -> X are functions, and h:X -> X is a one-to-one function such that f * h = g * h need it be the case that f = g? Prove it or give a counterexample. What if, in addition, X is finite? 3. The attempt at a solution I know that f does not equal g for an infinite set but is for a finite set. I know to prove that it isn't when it is infinite set it is the difference between the onto function. I am not sure how to relate that to the problem and build a proof out of it. Thanks!