AoPS Wiki:Problem of the Day/September 19, 2011

Let $f(f(x))=x$ , and let the points $(x,y)$ and $(y,z)$ be on the graph of $f(x)$ . Which of the following must be true?

$\textbf{ (A)}f(x)=2f(z)\quad \textbf{(B)}x=f(z)\quad \textbf{(C)}$ $f(x)=f(z) \quad \textbf{(D)}x=2y\quad \textbf{(E)}\text{None of the above}$

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