M := {f:[0,1] --> ℝ} ~+: M x M --> M

∀x∈[0,1]: (f~+g)(x) = f(x)+g(x)

I need to show that (M, ~+) is a group and answer additionally if its an abelian group.

The interval somehow just throws me off and I dont know how to start to proof anything.

(f~+g)(x) = f(x)+g(x) looks like group homomorphism to me.

A group has to be assoziative and it has an inverse/neutral element.

Where do I go from here?