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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Functions

NDA 2019 · Mathematics · Functions

Paragraph: Let f(x) = x^2 , g(x) = tan x and h(x) = ln x. Question:...

Paragraph: Let f(x) = x2x^2, g(x) = tan x and h(x) = ln x.
Question: For x=π2x=\frac{\sqrt{\pi}}{2}, what is the value of [ho(g∘f)](x)[h o(g {}^{\circ} f)](x) ?

Options

  1. A0
  2. B1
  3. Cπ4\frac{\pi}{4}
  4. Dπ2\frac{\pi}{2}

Correct answer

A. 0

Step-by-step solution

Given: f(x)=x2;f(x)=tan⁡xhf(x)=x^2 ; f(x)=\tan xh(x)=ln⁡x\ln x∴(ho(g∘f)x at x=π2=ln⁡(tan⁡(x2)=ln⁡(tan⁡π4)=ln⁡1=0\begin{aligned} & \therefore\left(h o(g {}^{\circ} f) x \text{ at } x=\frac{\sqrt{\pi}}{2}\right.\\ & =\ln \left(\tan \left(x^2\right)\right. \\ & =\ln \left(\tan \frac{\sqrt{\pi}}{4}\right)\\ & =\ln 1=0 \end{aligned}$$
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