\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that the set \(\mathcal{P}\) of even functions \(\mathbb{R} \to \mathbb{R}\) and the set \(\mathcal{I}\) of odd functions \(\mathbb{R} \to \mathbb{R}\) are two supplementary subspaces of \(\mathbb{R}^\mathbb{R}\).
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