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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Functions

NDA 2021 · Mathematics · Functions

What is the period of the function f(x)= (2+ ^2 x) ?

What is the period of the function f(x)=ln⁡(2+sin⁡2x)?f(x)=\ln \left(2+\sin ^2 x\right) ?

Options

  1. Aπ2\frac{\pi}{2}
  2. Bπ\pi
  3. C2π2 \pi
  4. D3π3 \pi

Correct answer

B. π\pi

Step-by-step solution

∴f(x+π)=ln⁡[2+sin⁡2(π+x)]=ln⁡[2+sin⁡2x]=f(x)f(x+2π)=ln⁡[2+sin⁡2(2π+x)]=ln⁡[2+sin⁡2x]=f(x)f(x+3π)=ln⁡[2+sin⁡2(3π+x)]=ln⁡[2+sin⁡2x]=f(x)\begin{aligned} & \therefore f(x+\pi)=\ln \left[2+\sin ^2(\pi+x)\right]=\ln \left[2+\sin ^2 x\right]=f(x) \\ & f(x+2 \pi)=\ln \left[2+\sin ^2(2 \pi+x)\right]=\ln \left[2+\sin ^2 x\right]=f(x) \\ & f(x+3 \pi)=\ln \left[2+\sin ^2(3 \pi+x)\right]=\ln \left[2+\sin ^2 x\right]=f(x) \end{aligned} and minimum value of π,2πand3π\pi, 2 \pi and 3 \pi is π\pi So, period π\pi is.
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