Solution
= Solution
{c}
\b[Exactly $a\ne0$ works.] For nonzero $a$, composition with $x\mapsto ax$ preserves smoothness, and the <support of a function> is $[-1/|a|,1/|a|]$, which is compact. For $a=0$ the result is the strictly positive constant $\phi(0)$ on all of $\mathbb R$, so it lacks <compact support> and is not a <test function>.