Floor , Absolute, Inverse, Sawtooth And Periodic Also

First of all, $m^2-3m+1≤1$ and $m^2-3m+1≥-1$ . The union of these inequalities shows $0≤m≤1$ and $2≤m≤3$ . Since the question asks for non-negative integral values, $m$ can be $0$ , $1$ , $2$ , or $3$ . Also, $⌊e^{m-4}⌋=0$ since $m=0$ , $1$ , $2$ , or $3$ are all less than $4$ . As a result, the latter part of the function becomes $0$ . Since for the $4$ possible values for $m$ , $arcsin(m^2-3m+1)$ is not $0$ and k* $sec(|x|*0.3333)$ is periodic for some real number $k$ , there are $4$ possible values for $m$ that make $f(x)$ periodic.