已知函数fx x

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已知函数fx x
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已知函数fx x
已知函数fx x

已知函数fx x
答:
x<=0,f(x)=x+2
x>0,f(x)=-x+2
函数f(x)是两条射线,见简图如下
不等式f(x)>=x^2>=0
显然,从图像可以看出:-2<=x<=2时,f(x)>=0
1)当x<=0时:f(x)=x+2>=x^2
x^2-x-2<=0
(x-2)(x+1)<=0
-1<=x<=2
所以:-1<=x<=0
2)当x>0时:f(x)=-x+2>=x^2
x^2+x-2<=0
(x+2)(x-1)<=0
-2<=x<=1
所以:0<x<=1
综上所述,不等式f(x)>=x^2的解集为[-1,1]


x<=0,f(x)=x+2
x>0,f(x)=-x+2
函数f(x)是两条射线,见简图如下
不等式f(x)>=x^2>=0
显然,从图像可以看出:-2<=x<=2时,f(x)>=0
1)当x<=0时:f(x)=x+2>=x^2
x^2-x-2<=0
(x-2)(x+1)<=0
-1<=x<=2
所以:-1<=x<=0
...

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x<=0,f(x)=x+2
x>0,f(x)=-x+2
函数f(x)是两条射线,见简图如下
不等式f(x)>=x^2>=0
显然,从图像可以看出:-2<=x<=2时,f(x)>=0
1)当x<=0时:f(x)=x+2>=x^2
x^2-x-2<=0
(x-2)(x+1)<=0
-1<=x<=2
所以:-1<=x<=0
2)当x>0时:f(x)=-x+2>=x^2
x^2+x-2<=0
(x+2)(x-1)<=0
-2<=x<=1
所以:0

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