Question

Let $f\left(x\right)=\cos 3x+\sin \sqrt{3x}$. Then $f\left(x\right)$ is

• A. a periodic function of period $2\pi$
• B. a periodic function of period $\sqrt{3\pi }$
• C. not a periodic function
• D. none of these

Answer 1

Answer: (C)

not a periodic function

Period of $\cos 3x$ is $\frac{2\pi }{3}$

Period of $\sin \left(\sqrt{3x}\right)$ is $\frac{2\pi }{\sqrt{3}}$

LCM of $\frac{2\pi }{3}$ and $\frac{2\pi }{\sqrt{3}}$ not possible.because HCf of rational and irrational not possible.
Therefore, period of $f\left(x\right)$ does not exist.

Hence, option 'C' is correct.