The range of the function $f(x) = \frac{x-3}{5-x}, x \neq 5$ is

The range of the function $f(x)=\sin [x]$,where $-\frac{\pi}{4} < x < \frac{\pi}{4}$ and $[x]$ denotes the greatest integer $\leq x$,is

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

The domain of the function $\log _{10}(x^2-5x+6)$ is

The domain of the function $f(x) = \sqrt{x-1} + \sqrt{6-x}$ is

Domain of the real valued function $f(x) = \frac{x+2}{9-x^{2}}$ is