 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-1/3e/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

No. Take

f (x) = {x, 2 x, x \geq 0, x < 0, g (y) = {2 y, y, y \geq 0, y < 0.

Both functions are nonconstant on every interval and nondifferentiable at zero, but

g (f (x)) = 2 x

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