Question

若函数f(X）的定义域为R,且对一切实数X,满足f(2+x)=f(2-x),f(7+x)=f(7-x) 求证：函数f(x

Answer 1

f(2+x)=f(2-x) ==> 令2-x=t ==> f(t)=f(4-t)

f(7+x)=f(7-x) ==> 令7-x=t ==> f(t)=f(14-t)

得f(4-t)=f(14-t)==> 令4-t=x ==> f(x)=f(x+10)

所以函数f(x)是周期为10