计算f(x)＝-(1/2)^2x+4(1/2)^x+5,是减函数.

Question

计算f(x)＝-(1/2)^2x+4(1/2)^x+5,是减函数.

Answer 1

令t=(1/2)^x.
f(t)=-t^2+4t+5=-(t-2)^2+9,则f(t)在(0,2)上增,在（2,正无穷）上减.
因t(x)在R上递减,则f(x)在(-1,正无穷）上减,在（负无穷,-1）上增
f(t)=-(t-2)^2+9(t>0),则f(t)