(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Combinatorial Theory (f*h=g*h) g=f?

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