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Let $C[-1,1]$ be the real inner product space consisting of all continuous functions $f:[-1,1] \rightarrow \mathbb{R}$, with the inner product $\langle f, g\rangle:=\int_{-1}^{1} f(x) g(x) d x$. Let $W$ be the subspace of odd functions, i.e. functions satisfying $f(-x)=-f(x)$. Find (with proof) the orthogonal complement of $W$.
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