R to R/Even and odd/Direct sum/Exercise

Let ${}V=\operatorname {Map} \,{\left(\mathbb {R} ,\mathbb {R} \right)}$ be the vector space of all functions from ${}\mathbb {R}$ to ${}\mathbb {R}$. Show that there exists a direct sum decomposition

${}V=G\oplus U\,,$

where ${}G$ denotes the linear subspace of all even functions, and ${}U$ denotes the linear subspace of all odd functions.

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