Question

若函數(shù)y=f(x)存在反函數(shù)y=f-1(x)，則下列命題中不正確的是(   )

A.若f(x)=f-1(x)，則函數(shù)y=f(x)的圖象關于y=x對稱

B.函數(shù)y=f(x)的圖象與直線y=x相交,則交點一定在它的反函數(shù)的圖象上

C.若函數(shù)y=f(x)是(-∞,+∞)上的減函數(shù),則其反函數(shù)y=f ^-1(x)也是(-∞,+∞)上的減函數(shù)

D.函數(shù)值域中的每一個值都有原象

Answer 1

C

解析:原函數(shù)y=f(x)是(-∞,+∞)上的減函數(shù),則其反函數(shù)y=f ^-1(x)是原函數(shù)值域上的減函數(shù).

因為y=f(x)的值域未必是(-∞,+∞),故C不正確.