若f(x)是偶函数,求f(1+更号2)-f(1减根号2 分之1)德值

问题描述:

若f(x)是偶函数,求f(1+更号2)-f(1减根号2 分之1)德值

f(1+√2)-f(1/(1-√2))
=f(1/(√2-1))-f(1/(1-√2))(分子有理化)
=f(1/(√2-1))-f(-1/(√2-1))
=f(1/(√2-1))-f(1/(√2-1))(偶函数)
=0