 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2011/ia/paper-1/10e/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

f (x) = 1

for

0 \leq x < 1

and

f (1) = 0

. This self-map of

[0, 1]

is discontinuous at one. Every point smaller than one is sent to a different point, and one is sent to zero, so it has no fixed point.

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