Cyclic function
Source: AMC 12 2006 A, Problem 18
February 5, 2006
functionalgebradomaincyclic functionAMC
Problem Statement
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\}