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infinitely many points of discontinuity

Source: Vietnam TST 1985 Problem 6

February 5, 2010
functionalgebrafunctional equationalgebra proposed

Problem Statement

Suppose a function f:R→R f: \mathbb R\to \mathbb R satisfies f(f(x)) \equal{} \minus{} x for all x∈R x\in \mathbb R. Prove that f f has infinitely many points of discontinuity.
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