# 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:

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