题目有问题啊,兄.
由x=o,a>=1;
由ax^2+bx+c=0;1-2a>=0,a谢谢提醒，已更正f(-1)=a-b+c=0,取x=1,1<=f(1)<=1,f(1)=a+b+c=1,b=0.5,a+c=0.5;ax^2+1/2x+(0.5-a)<=(x^2+1)/2,即(1-2a)x^2-x+2a>=0,1-4*(1-2a)*2a<=0,即（4a-1)^2<=0,a=1/4,c=1/4.