 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-2/2a/i/solution

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

x = y = 0

f (0) = \frac{2 f ( 0 )}{1 - f ( 0 ) ^{2}} .

The denominator is defined. If

f (0) \neq = 0

, cancellation would give

f (0)^{2} = - 1

, impossible for a real-valued function. Hence

f (0) = 0 .

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