已知函数f(x)=log2(1/x+1),x》0 且(1/2)^x-1, xf(a),则a的取值范围是多少?

问题描述:

已知函数f(x)=log2(1/x+1),x》0 且(1/2)^x-1, xf(a),则a的取值范围是多少?
要详细解答,给高分

f(x) = log2【1/(x+1)】,x≥0f(x) = (1/2)^x - 1,x<0当x≥0时,∵x+1单调增,∴1/(x+1)单调减,∴f(x)=log2(1/(x+1))单调减,x=0时最大值f(0)= log2【1/(0+1)】=0当xf(a)∴3-2a^2<a∴2a^2+a-3>0,即(2a+3)(a-1)>0∴a1...