1.g(x)=2^(x+2) - (a)/2^(x+2)
(無(wú)須詳解,函數(shù)圖像橫向移動(dòng)左加右減)
2.h(x)與g(x)關(guān)于y=1對(duì)稱
∴[h(x)+g(x)]/2=1
h(x)=2-g(x)=2-2^(x+2)+(a)/2^(x+2)
3.F(x)=(1/a)*f(x)+h(x)=[2^x - (a)/2^x](1/a)+2-2^(x+2)+(a)/2^(x+2)
=(1/a-4)*2^x+(a/4-1)*1/2^x+2
令y=2^x(y>0)
則F(y)=(1/a-4)y+(a/4-1)*1/y+2
根據(jù)圖像可知,當(dāng)(1/a-4)y=(a/4-1)*1/y時(shí),F(x)取最小值
m=1/2*根號(hào)[(a2-4a)/(1-4a)]+2
又 m＞2+根號(hào)7,
∴不等式組（a2+24a-7)/(1-4a)＞0,(a2-4a)/(1-4a)≥0
解之,得a的范圍