Difference between revisions of "2006 AMC 12A Problems/Problem 18"
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== Problem == | == Problem == | ||
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| + | The function <math>f</math> has the property that for each real number <math>x</math> in its domain, <math>1/x</math> is also in its domain and | ||
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| + | <math>f(x)+f\left(\frac{1}{x}\right)=x</math> | ||
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| + | What is the largest set of real numbers that can be in the domain of <math>f</math>? | ||
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| + | <math> \mathrm{(A) \ } \{x|x\ne 0\}\qquad \mathrm{(B) \ } \{x|x<0\}\qquad \mathrm{(C) \ } \{x|x>0\}</math><math>\mathrm{(D) \ } \{x|x\ne -1\;\mathrm{and}\; x\ne 0\;\mathrm{and}\; x\ne 1\}\qquad \mathrm{(E) \ } \{-1,1\}</math> | ||
== Solution == | == Solution == | ||
Revision as of 22:59, 10 July 2006
Problem
The function 
has the property that for each real number 
in its domain, 
is also in its domain and
What is the largest set of real numbers that can be in the domain of ?
