Difference between revisions of "2006 AMC 12A Problems/Problem 18"

Revision as of 23:02, 10 July 2006

The function $f$ has the property that for each real number $x$ in its domain, $1/x$ is also in its domain and

$f(x)+f\left(\frac{1}{x}\right)=x$

What is the largest set of real numbers that can be in the domain of $f$ ?

$\mathrm{(A) \ } \{x|x\ne 0\}\qquad \mathrm{(B) \ } \{x|x<0\}$

$\mathrm{(C) \ } \{x|x>0\}$ $\mathrm{(D) \ } \{x|x\ne -1\;\rm{and}\; x\ne 0\;\rm{and}\; x\ne 1\}$

$\mathrm{(E) \ } \{-1,1\}$

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 <math> \mathrm{(A) \ } \{x|x\ne 0\}\qquad \mathrm{(B) \ } \{x|x<0\}</math>
-<math>\mathrm{(C) \ } \{x|x>0\}</math><math>\mathrm{(D) \ } \{x|x\ne -1\;\mathrm{and}\; x\ne 0\;\mathrm{and}\; x\ne 1\}</math><math>\mathrm{(E) \ }  \{-1,1\}</math>
+<math>\mathrm{(C) \ } \{x|x>0\}</math><math>\mathrm{(D) \ } \{x|x\ne -1\;\rm{and}\; x\ne 0\;\rm{and}\; x\ne 1\}</math>
+<math>\mathrm{(E) \ }  \{-1,1\}</math>
 == Solution ==