Question

函數(shù)y=

1-x2

(-1≤x≤0)的反函數(shù)是（　　）

• A．y=

  1-x2

  (0≤x≤1)
• B．y=-

  1-x2

  (0≤x≤1)
• C．y=-

  x2-1

  (-2≤x≤-1)
• D．y=-

  1-x2

  (-1≤x≤0)

Answer 1

分析：由y=

1-x2

(-1≤x≤0)，知0≤y≤1，x=-

1-y2

，x，y互換，得函數(shù)y=

1-x2

(-1≤x≤0)的反函數(shù)是y=-

1-x2

(0≤x≤1)．

解答：解：∵y=

1-x2

(-1≤x≤0)，
∴0≤y≤1，
1-x²=y²，
x=-

1-y2

，
x，y互換，
得函數(shù)y=

1-x2

(-1≤x≤0)的反函數(shù)是y=-

1-x2

(0≤x≤1)．
故答案為：y=-

1-x2

(0≤x≤1)．

點(diǎn)評(píng)：本題考查反函數(shù)的求法，解題時(shí)要認(rèn)真審題，仔細(xì)解答，注意反函數(shù)的定義域是原函數(shù)的值域．