The domain of the function $f(x) = \sin^{-1}[\log_2(x/2)]$ is

The value of $\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)$ is

If the domain of the function $f(x) = \cos^{-1}(\frac{2x-5}{11-3x}) + \sin^{-1}(2x^2-3x+1)$ is the interval $[\alpha, \beta]$,then $\alpha + 2\beta$ is equal to:

If $A = \{x \in R : \sin^{-1}(\sqrt{x^2+x+1}) \in [-\frac{\pi}{2}, \frac{\pi}{2}]\}$ and $B = \{y \in R : y = \sin^{-1}(\sqrt{x^2+x+1}), x \in A\}$,then which of the following is true?

Domain of function $f(x) = \sin^{-1}(5x)$ is

The range of the real valued function $f(x) = \sin^{-1} ( \frac{1 + x^2}{2 x} ) + \cos^{-1} ( \frac{2 x}{1 + x^2} )$ is