函数f(x)是R上的偶函数, f(x)关于y轴对称。 f(x)在[0,正无穷)是单调递减,所以f(x)在(-无穷,0)单调递增。
f(-2) = 0 , 所以 f(2) = 0.
f(x)的图像,你可以认为是这样的:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/8c1001e93901213f5ef1eff057e736d12e2e95d8?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
(x-1)f(x) < 0
(1) x - 1>0时,即x>1时,f(x)<0;此时,看图,x<-2或x>2
所以:取 x>2.
(2) x - 1<0时,即x<1时,f(x)>0;此时,看图,-2<x<2
所以:取-2<x<1
综上解集为:
(-2,1)U(2,+无穷)
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