Question: Let (G, ) be a group and X any set. Define F to be the set of functions f : X G and define a

Let (G, ) be a group and X any set. Define F to be the set of functions f : X G and define a binary operation ? on F as follows: f ?g : X G is the function given by (f ?g)(x) := f(x)g(x) x X. Is (F, ?) a group? Justify your answer.

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