Given the general vector space, $F(-\infty,\infty)$, denoted V. Do even functions, $f(-x)=f(x)$, form a subspace of v?
2026-03-26 09:18:13.1774516693
Do functions $f$ in $F(-\infty,\infty)$ that satisfy $f(-x)=f(x)$ form a subspace of $F(-\infty,\infty)$?
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Yes: 1. $af(-x)=af(x)$. 2. $(f+g)(-x)=f(-x)+g(-x)=f(x)+g(x)=(f+g)(x)$.