Domain of function $f(x) = \log|5\{x\} - 2x|$ is $x \in R - A$,then $n(A)$ is (where $\{.\}$ denotes fractional part function)

The domain of the function $f(x) = \frac{\cot^{-1} x}{\sqrt{x^2 - [x^2]}}$,where $[x]$ denotes the greatest integer not greater than $x$,is :

Let $R$ be the set of real numbers and $f: R \rightarrow R$ be given by $f(x) = \sqrt{|x|} - \log(1 + |x|)$. We now make the following assertions:
$I.$ There exists a real number $A$ such that $f(x) \leq A$ for all $x$.
$II.$ There exists a real number $B$ such that $f(x) \geq B$ for all $x$.

Range of the function $f(x) = 3 + 2^x + 4^x$ is

If the function $f: R-\{-1, 1\} \rightarrow A$ defined by $f(x) = \frac{x^2}{1-x^2}$ is surjective,then $A$ is equal to

The range of the function $f(x) = \frac{\sqrt{1 - x^2}}{1 + |x|}$ is