Q45 / 120 · JEE Main 2007 · Mathematics

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

  • A
    $[0, \pi]$
  • B
    $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
  • C
    $\left[-\frac{\pi}{4}, \frac{\pi}{2}\right)$
  • Correct answer
    D
    $\left[0, \frac{\pi}{2}\right)$

Solution

$f(x)$ is defined if $-1 \leq \frac{x}{2}-1 \leq 1$ and $\cos x>0$ or $0 \leq x \leq 4$ and $-\frac{\pi}{2} < x < \frac{\pi}{2}$ $\therefore \mathrm{x} \in\left[0, \frac{\pi}{2}\right) \text {. }$

Hence, the correct answer is option: 'D'.

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