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

If the domain of the function $f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}}$ is $(a, b)$,then $(1+a)^2 + b^2$ is equal to :

The domain of the real valued function $f(x) = \sqrt{\frac{x-2}{3-x}}$ is...

The range of the function $f(x) = \log_{\sqrt{5}}(3 + \cos(\frac{3\pi}{4} + x) + \cos(\frac{\pi}{4} + x) + \cos(\frac{\pi}{4} - x) - \cos(\frac{3\pi}{4} - x))$ is:

The real-valued function $f(x) = \frac{\operatorname{cosec}^{-1} x}{\sqrt{x - [x]}}$,where $[x]$ denotes the greatest integer less than or equal to $x$,is defined for all $x$ belonging to:

The range of the function $f(x) = \frac{1}{\sqrt{x-[x]}}$ is