Question

设f(x)=lg1+2^x+4^xa/3,当x∈(-∞,1]时f(x)有意义,则a的取值范围是

Answer 1

设t=2^x,x∈(-∞,1],则t∈(0,2],

∵x∈(-∞,1]时f(x)有意义,

∴（at^2+t+1）/3>0,t∈(0,2],

∴a>-(t+1)/t^2

∵-(t+1)/t^2=-(1/t^2+1/t)=-(1/t+1/2)^2+1/4,1/t∈[1/2,+∞),

∴a≥-3/4