 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-2/12f/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Since

G_{X} (1) = 1

and

G_{X}^{'} (1) = μ > 1

, for

t < 1

sufficiently close to one,

G_{X} (t) - t < 0.

At zero,

G_{X} (0) - 0 \geq 0

. Continuity therefore gives a fixed point in

[0, 1)

, and part (b) implies

d < 1

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