Solution
= Solution
For $k>0$, $\int_k^\infty x^{-2}\,dx=1/k$. Thus the unnormalized <integral> is $1/k$ and the multiplicative normalization is $k$:
$$
\boxed{g(x)=\frac{k}{x^2}\mathbf1_{\{x\geq k\}}.}
$$
Although this proposal does not cover the whole <Cauchy distribution> <probability support>, it covers the entire nonzero integrand $f\theta$, which is the required <support condition for importance sampling>.