The largest interval lying in $(-\frac{π}{2},\frac{π}{2})$ for which the function $[f(x)=4^{-x^2}+\cos^{-1}(\frac{x}{2}-1)+\log(\cos x)]$ is defined, is:
Answer & explanation
Correct answer: option 4
$-1≤\frac{x}{2}-1≤1$ and $\cos x > 0$
$0 ≤ x ≤ 4$ and $0 ≤ x ≤ \frac{π}{2}$
$x∈[0,4],x∈[0,\frac{π}{2})$
$=x∈[0,\frac{π}{2})$