Difference between revisions of "AoPS Wiki:Problem of the Day/September 19, 2011"

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

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

Revision as of 16:07, 19 September 2011 (view source) Negativebplusorminus (talk \| contribs) (Created page with "Let <math>f(f(x))=x</math>, and let the point <math>(x,y)</math> and <math>(y,z)</math> are on the graph of <math>f(x)</math>. Which of the following must be true? <math>\textb...")		Revision as of 16:15, 19 September 2011 (view source) Negativebplusorminus (talk \| contribs) (Making it harder.) Newer edit →
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	Let <math>f(f(x))=x</math>, and let the point <math>(x,y)</math> and <math>(y,z)</math> are on the graph of <math>f(x)</math>. Which of the following must be true?		Let <math>f(f(x))=x</math>, and let the point <math>(x,y)</math> and <math>(y,z)</math> are on the graph of <math>f(x)</math>. Which of the following must be true?

−	<math>\textbf{ (A)}x=2z\quad \textbf{(B)}x=z^2\quad \textbf{(C)}x=z \quad \textbf{(D)}x=2y\quad \textbf{(E)}\text{None of the above}</math>	+	<math>\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}</math>