若已知f(x-1)是奇函数,那么是f(-x-1)=-f(x-1)还是f(-x+1)=-f(x-1)?

题目

若已知f(x-1)是奇函数,那么是f(-x-1)=-f(x-1)还是f(-x+1)=-f(x-1)?

答案

f(-x-1)=-f(x-1)
eg:
f(x-1)=x是奇函数,
令t=x-1,则f(t)=t+1,
f(-x-1)=f(-x+1-2)=f(-t-2)
=-t-2+1=-t-1
=-(x-1)-1
=-x
=-f(x-1)