Question:
The period of function $f(x)=| \sin 4x | + | \cos 4x |$ is
The period of function $f(x)=| \sin 4x | + | \cos 4x |$ is
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The period of function $f(x)=| \sin 4x | + | \cos 4x |$ is
Updated On: Apr 15, 2026
- $\pi/2$
- $\pi/8$
- $\pi/4$
- None of these
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The Correct Option is B
Solution and Explanation
Step 1: Concept
The function $g(x) = |\sin x| + |\cos x|$ is a periodic function with a period of $\pi/2$.
Step 2: Analysis
If a function $f(x)$ has period $T$, then $f(ax)$ has period $T/|a|$.
Step 3: Evaluation
Here, the base function is scaled by $a = 4$.
Step 4: Conclusion
Therefore, the period is $\frac{\pi/2}{4} = \pi/8$.
Final Answer: (b)
The function $g(x) = |\sin x| + |\cos x|$ is a periodic function with a period of $\pi/2$.
Step 2: Analysis
If a function $f(x)$ has period $T$, then $f(ax)$ has period $T/|a|$.
Step 3: Evaluation
Here, the base function is scaled by $a = 4$.
Step 4: Conclusion
Therefore, the period is $\frac{\pi/2}{4} = \pi/8$.
Final Answer: (b)
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