Let $f:\mathbb R\to \mathbb R, f(x) =\{\frac{x+1}{3}\}$, where { } is the fractional part.
So pretty much I have to find if this function is periodic. My first thought was this: We have ax + b so f is periodic with period $\frac{T}{a}$ (1)
We also know that {a}={a+k} so this means $\frac{x+1}{3}=\frac{x+1}{3}+T => T = 1 $ (2)
(1)+(2) => The function is periodic with period 3
But I'm not sure if this is true so I thought to ask you people. Thanks in advance.