y=4^(x-1/2)-a×2^x+(a/2)+1 ======>>>>>> 设:2^x=t,则:1≤t≤4
y=(1/2)t²-at+(a/2)+1
=(1/2)[t-a]²+[-a²+(1/2)a+1] =====>>>>>> 设这个函数的最小值是g(a),最大值是h(a)
则:
1、最小值
{ -(1/2)a+(3/2) a<1
g(t)= { -a²+(1/2)a+1 1≤a≤4
{ -(3/2)a+9 a>4
2、最大值
{ -(1/2)a+(3/2) a≥5/2
h(x)= { -(3/2)a+9 a<5/2