HMMT 2005 K10

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a smooth function such that $f^{\prime}(x)=f(1-x)$ for all $x$ and $f(0)=1$ . Find $f(1)$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\sec 1+\tan 1

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