If$f\left(x\right)=\cos \pi \left(\left|x\right|+\left[x\right]\right),$  then $f$ is (where $[.]$ denotes greatest integral function), then which is not rue

$f\left(x\right)=\left(\cos \pi \left|x\right|+\left[x\right]\right)=\{\begin{array}{c}\cos \pi \left(-x+\left(-1\right)\right),-1\le x<0\\ \cos \pi \left(x+0\right),0\le x<1\end{array}$

$=\{\begin{array}{c}-\cos \pi x,-1\le x<0\\ \cos \pi x,0\le x<1\end{array}$

Obviously, $f\left(x\right)$ s discontinuous at $x=0;$  otherwise, $f\left(x\right)$ is continuous and differentiable in $\left(-1,0\right)$ and $\left(0,1\right)$