Let $f(x)=nx+n-[nx+n]+\tan(\frac{πx}{2})$, where [x] is the greatest integer ≤ x and n ∈ N. It is

a periodic function of period 1 a periodic function of period 4 non-periodic a periodic function of period 2

a periodic function of period 2

$nx+n-[nx+n]$ has period 1/n and $\tan(\frac{1}{2}πx)$ has the period $\frac{π}{π/2}=2$ L.C.M of 1/n and 2 is 2 ∴ f(x) is a period function of period 2.