Question

若0＜x＜y＜1，則下列不等式成立的是（　�。�

• A、(

  1

  2

  )x＜(

  1

  2

  )y
• B、x-

  1

  3

  ＜y-

  1

  3

• C、log2x

  1

  2

  ＜log2y

  1

  2

• D、log

  1

  2

  x3＜log

  1

  2

  y3

Answer 1

分析：根據(jù)指數(shù)函數(shù)、對(duì)數(shù)函數(shù)、冪函數(shù)的單調(diào)性進(jìn)行驗(yàn)證即可．

解答：解：∵y=( 

1

2

) x是單調(diào)遞減函數(shù)且x＜y∴(

1

2

)x＞(

1

2

)y排除A
∵y=x-

1

3

在x＞0時(shí)單調(diào)遞減且0＜x＜y∴x-

1

3

＞y-

1

3

排除B．
y=log₂x單調(diào)遞增且0＜x＜y∴l(xiāng)og₂x＜log₂y∴

1

2

log2x＜

1

2

log2y∴log2x

1

2

＜log2y

1

2

故C對(duì)．
故選C．

點(diǎn)評(píng)：本題主要考查指數(shù)函數(shù)和對(duì)數(shù)函數(shù)的單調(diào)性．當(dāng)?shù)讛?shù)大于1時(shí)函數(shù)單調(diào)遞增，當(dāng)?shù)讛?shù)大于0小于1時(shí)函數(shù)單調(diào)遞減．