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smc

algebra senior

Problem

The domain of the function is an interval of length , where and are relatively prime positive integers. What is ?
(A)
(B)
(C)
(D)
Solution
For all real numbers and such that and note that: 1. is defined if and only if 2. For we conclude that:

  • if and only if 3. if and only if For we conclude that: 5. if and only if 6. if and only if Therefore, we have The domain of is an interval of length from which the answer is Remark This problem is quite similar to 2004 AMC 12A Problem 16.
    • Final answer
    C