2006 AMC 12A Problems/Problem 18: Difference between revisions
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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 | The function <math>\displaystyle f</math> has the property that for each real number <math>\displaystyle x</math> in its domain, <math>\displaystyle 1/x</math> is also in its domain and | ||
<math>f(x)+f\left(\frac{1}{x}\right)=x</math> | <math>f(x)+f\left(\frac{1}{x}\right)=x</math> | ||
Revision as of 00:21, 10 August 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 
?
Solution
Plugging in 
into the function:
Since 
cannot have two values:
Therefore, the largest set of real numbers that can be in the domain of is 
