2．已知函数f (x)的定义域是R,且f (2 - x) = - f (x + 2),若f (x)是奇函数,则f (x)的周期是 4 .
分析：∵f (2 - x) = - f (x + 2),
∴f(x+4)=f[(x+2)+2]=-f[2-(x+2)]=-f(-x),
又f (x)是奇函数,得f(-x)= - f(x),
∴f(x+4)= -f(-x)=f(x),T=4.
3.已知函数f (x)的定义域是R,且f (2 - x) = - f (x + 2),若f (x)是偶函数,则f (x)的周期是 8 .
分析：∵f (2 - x) = - f (x + 2),
∴f(x+4)=f[(x+2)+2]=-f[2-(x+2)]=-f(-x),
又f (x)是偶函数,得f(-x)= f(x),
∴f(x+4)= -f(-x)=-f(x),
f(x+8)=f[(x+4)+4]=-f(x+4)=f(x),T=8.
4．已知函数f (x)的定义域是R,且f (2 - x) = - f (x + 2),若f (1+ x) = f (1- x),则f (x)的周期是 4 .
分析：∵f (1+ x) = f (1- x),
∴f(2-x)=f[1+(1-x)]=f[1-(1-x)]=f(x),
又f (2 - x) = - f (x + 2),
∴f(x+2)=-f(x),
f(x+4)=f[(x+2)+2]=-f(x+2)=f(x),T=4.