Difference between revisions of "2006 AMC 12A Problems/Problem 18"
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== Solution == | == Solution == | ||
| + | Quickly verifying by plugging in values verifies that <math>-1</math> and <math>1</math> are in the domain. | ||
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<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 15:18, 1 November 2013
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
Quickly verifying by plugging in values verifies that 
and 
are in the domain.
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 
See also
| 2006 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 17 |
Followed by Problem 19 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
