Question

已知函數(shù)是上的單調(diào)增函數(shù)且為奇函數(shù)，數(shù)列是等差數(shù)列，，則的值（    ）

A．恒為正數(shù)                                                                     B．恒為負(fù)數(shù)

C．恒為0                                                                           D．可以為正數(shù)也可以為負(fù)數(shù)

 

Answer 1

【答案】

 

【解析】

試題分析：因為函數(shù)是上的奇函數(shù),所以又是上的增函數(shù),所以當(dāng) 時有,當(dāng) 時有,因為所以有 .

因為數(shù)列是等差數(shù)列,所以 又,所以 ,即有

考點：函數(shù)的單調(diào)性應(yīng)用,奇函數(shù)的性質(zhì),等差中項的應(yīng)用.