Question

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

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

Answer 1

Answer: (D)

$f (x)$ is defined if $-1\le \frac{x}{2}-1\le1$ and $cos x > 0$
or $0 \le x \le 4$ and $-\frac{\pi}{2} < x < \frac{\pi}{2}$
$\therefore x\,\in0, [\frac{\pi}{2})$