$\left\{x \in R: \frac{2 x-1}{x^3+4 x^2+3 x} \in R\right\}$ equals

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

The domain of the definition of the function $f(x) = \sqrt{\frac{4 - x^2}{[x] + 2}}$ is (where $[.] \rightarrow \text{G.I.F.}$)

The domain of definition of the function $f(x)$ given by the equation $2^x + 2^y = 2$ 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 $x$.

The domain of a function $f(y) = \frac{\cos^{-1}(y-5)}{\sqrt{25-y^2}}$ is