不等式一题求解第二问
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(2)易知f(x)>=0,∴a>=1/2,
f(x)={2x+a,x>=0;
.......{a,-a<x<0;
.......{-2x-a,x<=-a.
f(x)<=2a-1化为3个不等式组:
1)x>=0,2x+a<=2a-1;
2)-a<x<0,a<=2a-1;
3)x<=-a,-2x-a<=2a-1.由1)0<=x<=(a-1)/2;由2),-a<x<0,a>=1;由3),(1-3a)/2<=x<=-a.
综上,a>=1,(1-3a)/2<=x<=(a-1)/2,
依题意(a-1)/2-(1-3a)/2=2a-1=3,a=2,
b=(1-3a)/2=-5/2.
f(x)={2x+a,x>=0;
.......{a,-a<x<0;
.......{-2x-a,x<=-a.
f(x)<=2a-1化为3个不等式组:
1)x>=0,2x+a<=2a-1;
2)-a<x<0,a<=2a-1;
3)x<=-a,-2x-a<=2a-1.由1)0<=x<=(a-1)/2;由2),-a<x<0,a>=1;由3),(1-3a)/2<=x<=-a.
综上,a>=1,(1-3a)/2<=x<=(a-1)/2,
依题意(a-1)/2-(1-3a)/2=2a-1=3,a=2,
b=(1-3a)/2=-5/2.
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