 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ia/paper-2/2d/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

F (x) = ∣ x^{3} - x ∣

. The relation is exactly

x \sim y ⟺ F (x) = F (y) .

It is therefore the equivalence relation induced by a function: equality of the two function values is reflexive, symmetric, and transitive. Hence this is an equivalence relation.

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