The largest interval lying in , 2 2 æ ö -p p ç ÷ è ø for which the function, 2 1 ( ) 4 cos 1 log (cos ) 2 x x f x x – – æ ö = + -+ ç ÷ è ø , is defined, is

Question:

The largest interval lying in $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ for which the function, $f(x)=4^{-x^{2}}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)$, is defined, is

  1. $\left[-\frac{\pi}{4}, \frac{\pi}{2}\right)$

  2. $\left[0, \frac{\pi}{2}\right)$

  3. $[0, \pi]$

  4. $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$


Correct Option: 2

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year 2007

Solution:

Related Questions

  • If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0<\alpha, \beta<\frac{\pi}{2}$, then $\alpha-\beta$ is equal to:

    View Solution

  • A value of $x$ satisfying the equation $\sin \left[\cot ^{-1}(1+x)\right]=\cos$ $\left[\tan ^{-1} x\right]$, is :

    View Solution

  • The principal value of $\tan ^{-1}\left(\cot \frac{43 \pi}{4}\right)$ is:

    View Solution

  • The number of solutions of the equation, $\sin ^{-1} x=2 \tan ^{-1} x$ (in principal values) is :

    View Solution

  • A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

    View Solution

  • A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

    View Solution

  • The domain of the function $f(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}}$ is

    View Solution

  • The trigonometric equation $\sin ^{-1} x=2 \sin ^{-1} a$ has a solution for

    View Solution

  • $$

    \cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x

    $$ then $\sin x=$

    View Solution

  • The domain of $\sin ^{-1}\left[\log _{3}(x / 3)\right]$ is

    View Solution

Leave a Reply

Your email address will not be published.

error: Content is protected !!
Download App