Question

Period of the function $f\left(x\right)=\sin \left(\sin \right(\pi x\left)\right)+e^{\left\{3x\right\}}$, where $\{\cdot \}$ denotes the fractional part of $x$, is:

• A. $1$
• B. $2$
• C. $3$
• D. none of these

Answer 1

The correct option is B $2$

As $\sin \left(\pi x\right)$ has period $=\left|\frac{2\pi }{\pi }\right|=2$
$\therefore \sin \left(\sin \right(\pi x\left)\right)$ has period $2$
And $e^{\left\{3x\right\}}$ has period $\frac{1}{3}$.
$\therefore$ Period of $f\left(x\right)=\sin \left(\sin \right(\pi x\left)\right)+e^{\left\{3x\right\}}$ is
LCM of $\{2,\frac{1}{3}\}=2$
Hence, option 'B' is correct.