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

(Created page with "We know that <math>f(f(x))=x</math> for this particular function. Since <math>(x,y)</math> is on the graph, <math>y=f(x)</math>; since <math>(y,z)</math> is on the graph, <math>...")
 
 
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We know that <math>f(f(x))=x</math> for this particular function.  Since <math>(x,y)</math> is on the graph, <math>y=f(x)</math>; since <math>(y,z)</math> is on the graph, <math>z=f(y)=f(f(x))=x</math>, so the answer is <math>\boxed{\textbf{(C)}}</math>.
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We know that <math>f(f(x))=x</math> for this particular function.  Since <math>(x,y)</math> is on the graph, <math>y=f(x)</math>; since <math>(y,z)</math> is on the graph, <math>z=f(y)=f(f(x))=x</math>.  Thus, <math>f(x)=f(z)</math>, so the answer is <math>\boxed{\textbf{(C)}}</math>.

Latest revision as of 16:16, 19 September 2011

We know that $f(f(x))=x$ for this particular function. Since $(x,y)$ is on the graph, $y=f(x)$; since $(y,z)$ is on the graph, $z=f(y)=f(f(x))=x$. Thus, $f(x)=f(z)$, so the answer is $\boxed{\textbf{(C)}}$.

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