we have Abb(X) = {f | f : X −→ R} (f + g)(x) := f(x) + g(x) and (αf)(x) := α · f(x), for x ∈ X andα ∈ R. and we have G := {f : R −→ R | f(x) = f(−x) for x ∈ R} U := {f : R −→ R | f(x) = −f(−x) for x ∈ R} prove that G ⊕ U = Abb(R)

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