The range of $f(x) = [\cos x + \sin x]$ is (Where $[.]$ is $G.I.F.$)
$[-\sqrt 2 ,\sqrt 2 ]$
$\{0, 1, 2\}$
$\{-1, 0, 1\}$
$\{-2. -1, 0, 1\}$
Range of $f(x) = \;[x]\; - x$ is
Range of the function $f(x) = \frac{{{x^2}}}{{{x^2} + 1}}$ is
Domain of the function $f(x) = {\sin ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right) + {\cos ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right) + {\tan ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right)$ is
Set of all values of $x$ satisfying
$\frac{{{x^4} - 4{x^3} + 3{x^2}}}{{({x^2} - 4)({x^2} - 7x + 10)}} \ge 0$
If the domain of the function $f(\mathrm{x})=\frac{\cos ^{-1} \sqrt{x^{2}-x+1}}{\sqrt{\sin ^{-1}\left(\frac{2 x-1}{2}\right)}}$ is the interval $(\alpha, \beta]$, then $\alpha+\beta$ is equal to: