 Solution

ID: past-exam-of-the-short-options-course-of-the-university-of-oxford/2021/5/a/i/1/solution

Every $a \in R$ works. Translation preserves a smooth function, and the support of a function becomes the compact interval

[a - 1, a + 1]

. Hence

ϕ (\cdot - a) \in C_{c}^{\infty} (R)

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