已知f(x)是定义在R上以2为周期的函数,当0≤x≤1时,f(x)=log1/2(1-x),则f(-2014/4)=

问题描述:

已知f(x)是定义在R上以2为周期的函数,当0≤x≤1时,f(x)=log1/2(1-x),则f(-2014/4)=

解由函数的周期T=2
故f(-2014/4)
=f(-1007/2)
=f(-1007/2+504)
=f(1/2)
=log1/2(1-1/2)
=log1/2(1/2)
=1