Let F1 and F2 be fields. A function g ∈ F(F1, F2) is called an even function if g(−t) = g(t) for each t ∈ F1 and is called an odd function if g(−t) = −g(t) for each t ∈ F1. Prove that the set of all even functions in F(F1, F2) and the set of all odd functions in F(F1, F2) are subspaces of F(F1, F2).
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