Question

请证明一下‘若f(x)满足 f(x+T) = - f(x),则f(x)是周期为2T的周期函数.’

Answer 1

把f(x+T)看成f(y)

f(x+2T) = f((x+T)+T)= f(y+T)= - f(y)= - [f(x+T)] =-[-f(x)]=f(x)

f(x+2T) = f(x)所以是周期2T的周期函数