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Gaokao Math Practice Question

设函数 $f^{\prime}(x)$ 是奇函数 $f(x)(x \in R)$ 的导函数, $f(-1)=0$, 当 $x$ $>0$ 时, $x f^{\prime}(x)-f(x)<0$, 则使得 $f(x)>0$ 成立的 $x$ 的取值范围是 ($\qquad$)

  1. A.$(-\infty,-1) \cup(0,1)$
  2. B.$(-1,0) \cup(1,+\infty)$
  3. C.$(-\infty,-1) \cup(-1,0)$
  4. D.$(0,1) \cup(1,+\infty)$

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