Let I = (π, π) be the open interval and consider the R vector space Diff (I, R) = {f: I → R : ƒ is differentiable for all t € I} Consider the two subsets Even (I, R) = {fe Diff(I, R) : ƒ(t) = f(−t) for all t € I} Odd(I, R) = {f € Diff(I, R) : f(t) = −ƒ(−t) for all t e I} Prove that Even (I, R), and Odd(I, R) are subspaces (b) Prove that Diff (I, R) = Even (I, R) + Odd(I, R) (a)

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