18
Part of 2006 AMC 12/AHSME
Problems(2)
Cyclic function
Source: AMC 12 2006 A, Problem 18
2/5/2006
The function has the property that for each real number in its domain, is also in its domain and
f(x) \plus{} f\left(\frac {1}{x}\right) \equal{} x.
What is the largest set of real numbers that can be in the domain of ?
(A) \{ x | x\ne 0\} \qquad (B) \{ x | x < 0\} \qquad (C) \{ x | x > 0\}\\
(D) \{ x | x\ne \minus{} 1 \text{ and } x\ne 0 \text{ and } x\ne 1\} \qquad (E) \{ \minus{} 1,1\}
functionalgebradomaincyclic functionAMC
Moving Lattice Point
Source: AMC 12 2006B, Problem 18
2/17/2006
An object in the plane moves from one lattice point to another. At each step, the object may move one unit to the right, one unit to the left, one unit up, or one unit down. If the object starts at the origin and takes a ten-step path, how many different points could be the final point?
analytic geometryAMC