Question

The period of the function $f\left(x\right)=x-[x-b]$ is

Answer 1

$f\left(x\right)=x-[x-b]$
$\Rightarrow f\left(x\right)=x-b-[x-b]+b$
$\Rightarrow f\left(x\right)=$ $\{x-b\}+b$ where $\{.\}$ is fractional function.
We know that fractional part function is periodic with a period $1$
So, period of $f\left(x\right)$ is $1$