Mathematics - Functions Question with Solution | TestHub

The period of $x-\lfloor x\rfloor$ is 1.

The period of $x-\lfloor x\rfloor$ is 1.

The period of $(x-\lfloor x\rfloor {)}^2$ is 1.

The period of $\sin (\pi x)$ is $\frac{2\pi }{\pi }=2$.

The period of $\cos (\pi x)$ is $\frac{2\pi }{\pi }=2$.

The period of $\tan (\pi x)$ is $\frac{\pi }{\pi }=1$.

Thus, each of the above functions is a periodic function. Therefore, their L.C.M. is 2. Hence, the function $f(x)$ is periodic with a fundamental period of 2.