A function f (t) from ℝ to ℝ is called even if f (−t) = f (t), for all t in ℝ , and odd if f (−t) = −f (t), for all t. Are the even functions a subspace of F(ℝ ,ℝ ), the space of all functions from ℝ to ℝ ? What about the odd functions? Justify your answers carefully.
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