Question

The largest interval lying in $\bigg \lgroup-\frac{\pi}{2},\frac{\pi}{2}\bigg \rgroup$ for which the function, $f(x)=4^{-x^{2}}+\cos^{-1}\bigg \lgroup \frac{x}{2}-1\bigg \rgroup +log(\cos x)$ is defined, is
(a) $\bigg [-\frac{\pi}{4},\frac{\pi}{2}\bigg \rgroup$(b) $\bigg [0,\frac{\pi}{2}\bigg \rgroup$
(c) [0, π]
(d) $\bigg \lgroup-\frac{\pi}{2},\frac{\pi}{2}\bigg \rgroup$

Answer 1

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

(a) $\bigg [-\frac{\pi}{4},\frac{\pi}{2}\bigg \rgroup$(b) $\bigg [0,\frac{\pi}{2}\bigg \rgroup$

(c) [0, π]

(d) $\bigg \lgroup-\frac{\pi}{2},\frac{\pi}{2}\bigg \rgroup$