f(x)={x} where {x}=x-[x] is periodic.

[spartas]

Find periodicity of the function f(x)=a{x} and f(x)={ax}
* f(x)={x}=x-[x]
[x]=k , k<x<k+1
[x+1]=k+1=[x]+1
f(x+T)={x+1}=x+1-[x+1]=x+1-([x]+1)=x-[x]=f(x)

 

[Deleted member 4993]

Find periodicity of the function f(x)=a{x} and f(x)={ax}
* f(x)={x}=x-[x]
[x]=k , k<x<k+1
[x+1]=k+1=[x]+1
f(x+T)={x+1}=x+1-[x+1]=x+1-([x]+1)=x-[x]=f(x)

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