The period of the function $\text{f(x)=}\left[6\mathrm{x}+7\right]\text{+cosπx-6x,}$where $\left[.\right]$ denotes the greatest integer function, is

$\text{⨍ (x)=}\left[6\mathrm{x}+7\right]\text{+cosπx-6x=}\left[6\mathrm{x}\right]\text{+7+cosπx-6x=7+cosπx-}\left\{6\mathrm{x}\right\}$

$\left\{6\mathrm{x}\right\}$ has period 1/6 and $\mathrm{cos\pi x}$ has period is  2. 
The period of $\text{f(x)=LCM}$ of 2 and 1/6=2