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0552 algebra 5th edition Round 5 p2

Source:

May 6, 2021
algebrainequalitiesfunction5th edition

Problem Statement

Prove or disprove the existence of a function f:S→Rf : S \to R such that for all x≠y∈Sx \ne y \in S we have ∣f(x)−f(y)∣≥1x2+y2|f(x) - f(y)| \ge \frac{1}{x^2 + y^2}, in each of the cases: a) S=RS = R b) S=QS = Q.
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