 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/ii/paper-3/2f/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-05

Let

e = (1, 0)

g (x) = {e, x, x = 0, x \neq = 0.

Then

∥ g (x) - x ∥ \leq 1

everywhere, but

0

0

, giving a bounded-displacement map which is not surjective.

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