The domain of the function $f(x) = [\log_{10}(\frac{5x - x^2}{4})]^{1/2}$ is

For $f(x) = \frac{\sin \pi[x]}{1+[x]} + \frac{x}{2+3x}$,where $[x]$ denotes the greatest integer function,the domain and range in $R$ are respectively

Let $f(x)=\sqrt{2-x-x^2}$ and $g(x)=\cos x$. Which of the following statements are true?
$I$. Domain of $f((g(x))^2) = \text{Domain of } f(g(x))$
$II$. Domain of $f(g(x)) + g(f(x)) = \text{Domain of } g(f(x))$
$III$. Domain of $f(g(x)) = \text{Domain of } g(f(x))$
$IV$. Domain of $g((f(x))^3) = \text{Domain of } f(g(x))$

The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - [x] - 6}}$,where $[x]$ is the greatest integer function $\leq x$,is:

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection, then $B$ is equal to

If $A \subseteq Z$ and the function $f: A \rightarrow R$ is defined by $f(x) = \frac{1}{\sqrt{64 - (0.5)^{24 + x - x^2}}}$,then the sum of all absolute values of elements of $A$ is