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【简答题】
对于函数f 1 (x),f 2 (x),h(x),如果存在实数a,b使得h(x)=a?f 1 (x)+b?f 2 (x),那么称h(x)为f 1 (x),f 2 (x)的生成函数. (Ⅰ)下面给出两组函数,h(x)是否分别为f 1 (x),f 2 (x)的生成函数?并说明理由; 第一组: f 1 (x)=sinx, f 2 (x)=cosx,  h(x)=sin(x+ π 3 ) ; 第二组:f 1 (x)=x 2 -x,f 2 (x)=x 2 +x+1,h(x)=x 2 -x+1; (Ⅱ)设 f 1 (x)=lo g 2 x, f 2 (x)=lo g 1 2 x,  a=2,  b=1 ,生成函数h(x).若不等式3h 2 (x)+2h(x)+t<0在x∈[2,4]上有解,求实数t的取值范围; (Ⅲ)设 f 1 (x)=x, f 2 (x)= 1 x (1≤x≤10) ,取a=1,b>0,生成函数h(x)使h(x)≥b恒成立,求b的取值范围.
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