The domain of the function defined by $f(x) = \cos^{-1} \sqrt{x-1}$ 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 $y = \tan^{-1} x$,then . . . . . . .

The function $f(x) = \sin^{-1}(\sqrt{x})$ is defined in the interval:

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

Considering only the principal values of the inverse trigonometric functions,the domain of the function $f(x) = \cos^{-1}\left(\frac{x^{2}-4x+2}{x^{2}+3}\right)$ is: