<p>The period of the function $f(x) = \sin(\sin(\pi x)) + e^{\{3x\}}$, where $\{.\}$ denotes the fractional part of $x$ is</p>
Step-by-Step Solution
Key Concept: The period of a sum of functions is the LCM of their individual periods, considering both sinusoidal and fractional part functions.
<p><strong>Solution:</strong></p><p>$\sin(\pi x)$ has period $\frac{2\pi}{\pi} = 2$.</p><p>Thus, $\sin(\sin(\pi x))$ has period $2$.</p><p>$e^{\{3x\}}$ has period $\frac{1}{3}$.</p><p>Period of $f(x) = \sin(\sin(\pi x)) + e^{\{3x\}}$ is $\text{LCM}(2, \frac{1}{3}) = 2$.</p><p>Hence, (b) is the correct answer.</p>
Correct Answer: b