2001 AMC 12 Problems/Problem 9
Problem
Let be a function satisfying for all positive real numbers and . If , what is the value of ?
Solution 1
Letting and in the given equation, we get , or .
Solution 2
The only function that satisfies the given condition is , for some constant . Thus, the answer is .
Solution 3
Note that the equation given above is symmetric, so we have . Plugging in and gives .
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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All AMC 12 Problems and Solutions |
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