The function f(x) = |sin 4x| + |cos 2x| is a | vedclass

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(B) Let $f(x) = |\sin 4x| + |\cos 2x|$.We know that the period of $|\sin ax|$ is $\frac{\pi}{|a|}$ and the period of $|\cos ax|$ is $\frac{\pi}{|a|}$.

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(B) Let $f(x) = |\sin 4x| + |\cos 2x|$.We know that the period of $|\sin ax|$ is $\frac{\pi}{|a|}$ and the period of $|\cos ax|$ is $\frac{\pi}{|a|}$.For $|\sin 4x|$,the period is $T_1 = \frac{\pi}{4}$.For $|\cos 2x|$,the period is $T_2 = \frac{\pi}{2}$.The period of the sum of two periodic functions is the least common multiple $(LCM)$ of their individual periods.$T = 	ext{LCM}\left(\frac{\pi}{4}, \frac{\pi}{2}ight) = \frac{	ext{LCM}(\pi, \pi)}{	ext{HCF}(4, 2)} = \frac{\pi}{2}$.Thus,the period of $f(x)$ is $\frac{\pi}{2}$.

The function $f(x) = |\sin 4x| + |\cos 2x|$ is a periodic function with period

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