 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-1/7h/b/solution

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

Because

x \mapsto c^{T} x

g (t x + (1 - t) y) = f (t c^{T} x + (1 - t) c^{T} y) \leq t f (c^{T} x) + (1 - t) f (c^{T} y) .

Hence composition of a convex function with an affine map is convex, and $g$ is convex.

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