Question

设f(x)=则不等式f(x)＞2的解集为(    )

A.(1,2)∪(3,+∞)                                B.(,+∞)

C.(1,2)∪(,+∞)                          D.(1,2)

Answer 1

思路解析:(1)x＜2时,f(x)=2e^x-1＞2e^x-1＞1=e⁰x＞1.

∴1＜x＜2.

(2)x≥2时,f(x)=log₃(x²-1)＞2log₃(x²-1)＞log₃9x²-1＞9x²＞x＞或x＜-x＞.

故综合(1)(2)有1＜x＜2或x＞.

答案:C