Question

函數(shù)y=ln

x

x-1

(x＞1)的反函數(shù)是（　　）

• A．y=

  ex

  ex-1

  (x＜0)
• B．y=

  ex-1

  ex

  (x＞0)
• C．y=

  ex

  ex-1

  (x＞0)
• D．y=

  ex-1

  ex

  (x＜0)

Answer 1

分析：由y=ln

x

x-1

(x＞1)求出x，然后把x和y互換即可得到答案．

解答：解：由y=ln

x

x-1

(x＞1)，得

x

x-1

=ey，解得x=

ey

ey-1

(y＞0)．
∴函數(shù)y=ln

x

x-1

(x＞1)的反函數(shù)是y=

ex

ex-1

(x＞0)．
故選C．

點(diǎn)評(píng)：本題考查了函數(shù)的反函數(shù)的求法，關(guān)鍵是注意反函數(shù)的定義域是原函數(shù)的值域，是基礎(chǔ)題．