Period of the function $f(x)=[6x + 7] + \cos πx − 6x$ where [.] denotes greatest integer function, is

2

$f (x)=[6x + 7] + \cos πx − 6x =[6x] + 7 + \cos πx − 6x$

$f (x)=[6x] − 6x + \cos πx + 7$

$f (x)= −\{6x\}+ \cos πx + 7$

Period of $\cos πx = 2$ and period of {(6x)} is $\frac{1}{6}$

and LCM of 2 and $\frac{1}{6}$ is 2. So period of f(x) is 2.