已知函数【y=x的负二次方】,它在(0,+00)和(—00,0)上是增函数还是减函数.
人气:242 ℃ 时间:2020-03-30 18:41:37
解答
函数y=x^(-2)=1/x²
x∈(-∞,0)时,设x1则y1-y2
=1/x1²-1/x2²
=(x2²-x1²)/(x1²x2²)
=(x2-x1)(x1+x2)/(x1²x2²)
而x2-x1>0,x1+x2<0
所以,y1x∈(0,+∞)时,设0则y1-y2
=1/x1²-1/x2²
=(x2²-x1²)/(x1²x2²)
=(x2-x1)(x1+x2)/(x1²x2²)
而x2-x1>0,x1+x2>0
所以,y1>y2,函数递减
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