1. Let $f(x)$ be an odd function defined on $(-\infty, 0) \cup(0$, $+\infty)$. When $x>0$, $x f^{\prime}(x)<0$ and $f(1)=0$. Then the solution set of the inequality $x f(x)<0$ is $\qquad$
$-1 .(-\infty,-1) \cup(1,+\infty)$.
When $x>0$, $x f^{\prime}(x)1$ or $10$.
Therefore, the solution set of the inequality $x f(x)<0$ is
$$
(-\infty,-1) \cup(1,+\infty) \text {. }
$$