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

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.