 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ib/paper-3/15a/a/solution

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

f

u = αx

gives

\int_{- \infty}^{\infty} f (x) δ (αx) d x = \frac{1}{∣ α ∣} f (0) .

Equality of distributions therefore gives

δ (αx) = ∣ α ∣^{- 1} δ (x) .

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