求函数f(x)=-(log1/2 2x)²-log1/4 x+5在2≤x≤4时的值域

换元法即可t=log2(x)∵ 2≤x≤4∴ 1≤t≤2又 log(1/2) 2x=log(1/2)2+log(1/2) x=-1-tlog(1/4)x=-log4(x)=-(1/2)log2(x)=-(1/2)t∴ f(x)=-(-1-t)²+(1/2)t+5=-(t+1)²+(1/2)t+5=-t²-(3/2)t+4=-(t+3/4)&#...