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

The range of the function $f(x)=-\sqrt{5-6x-x^2}$ is

The domain of the function defined by $f(x) = \frac{-5}{4x^2+1} + \sqrt{x^2-4}$ is

If the domain of the greatest integer function is the set of real numbers,then the range will be the set of

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