Periodic Functions

The function $f\left(x\right)$ satisfies the equation $f(x+1)+f(x-1)=\sqrt{3}f\left(x\right)\forall x\in R$, if $p$ is the period of $f\left(x\right)$,  then $(p-4)$ is equal to......

Period of the function $f\left(x\right)=\cos \left(\cos \pi x\right)+e^{\left\{4x\right\}}$, where $\{.\}$ denotes the fractional part of $x$, is - 

Let $f\left(x\right)=\sin ax+\cos bx$ be a periodic function, then

Which of the following function is periodic?

If $f\left(x\right)={\sin }^{2}x$ and $g\left(x\right)=\left\{x\right\}$ are two real valued function then

Let us consider a function $f\left(x\right)=\sin \left[x\right]$, where $\left[x\right]$ denotes the greatest integer function. Then

Which of the following functions are periodic?

If $\tan ax+\cot ax$ and $\left|\tan x\right|+\left|\cot x\right|$ are periodic functions of the same fundamental period then $a$ equals

Consider that the graph of $y=f\left(x\right)$ is symmetric about the lines $x=2$ and $x=4$ then the period of $f\left(x\right)$ is

Identify the correct statement

Let $f\left(x\right)=\left|\sin x\right|+\left|\cos x\right|,g\left(x\right)=\cos \left(\cos x\right)+\cos \left(\sin x\right)$,  $h\left(x\right)=\left\{-\frac{x}{2}\right\}+\sin \pi x$, where$\{ \}$ represents the fractional function, then the fundamental period of

If $f(x+10)+f(x+4)=0$, there $f\left(x\right)$ is a periodic function with period

Which of the following function is a periodic function?

The period of the function$f\left(x\right)=\sin x+\tan \frac{x}{2}+\sin \frac{x}{4}+\tan \frac{x}{8}+\dots +\sin \left(\frac{x}{2^{n-1}}\right)+\tan \left(\frac{x}{2^n}\right)$ is given by

The period of the function $f\left(x\right)=\sin \left(\frac{\pi x}{(n+1)!}\right)-\sin \left(\frac{\pi x}{n!}\right)$ is given by

The period of the function $f\left(x\right)={\sin }^{4}x+{\cos }^{4}x$ is

The period of the function $f\left(x\right)=3+\frac{4}{7}\sin \left(\frac{2x-3}{4}\right)$ is