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"PA. Let V (R) be a vector space of all functions from \\( R \\) to R.\nShow that \\( W _ { 1 } \\) and \\( W _ { 2 } \\) are subspaces of \\( V ( R ) \\)\nwhere \\( W _ { 1 } = \\{ f | f \\in V \\text { and } f ( - x ) = f ( x ) \\} \\)\n\\[ \\begin{aligned} \\text { Where } W _ { 1 } & = \\{ f | f \\in V \\text { and } f ( - x ) = f ( x ) \\} \\\\ & = \\text { The set of all even functions } \\\\ \\text { and } W _ { 2 } & = \\{ f | f \\in V \\text { and } f ( - x ) = - f ( x ) \\} \\\\ & = \\text { The set of all odd functions } \\end{aligned} \\]"

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