1.Ifafunctionhasaninversefunction,thentheinversefunctionisone-to-one.2.Ifafunctionisdiffrentiable,thef'(x)isone-to-one.需要理由和举例.

Question

1.If a function has an inverse function,then the inverse function is one-to-one.
2.If a function is diffrentiable,the f'(x) is one-to-one.
需要理由和举例.

Answer 1

第一个是对的!存在反函数的条件是原函数必须是一一对应的,也就是说原函数有反函数,则反函数一定是一一对应的!
第二个是错的!可微分的函数太多了!x的三次方,微分后是d（x^3)=3x^2 dx其中3x^2是3x^2就是f'(x),显而易见,他不是one to one 的!