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

If the range of the real valued function $f(x) = \frac{x^2+x+k}{x^2-x+k}$ is $\left[\frac{1}{3}, 3\right]$,then $k=$

Let $f : R \to R$ be defined by $f(x) = \frac{x}{1 + x^2}, x \in R$. Then the range of $f$ is

For the function $f(x) = \left[ \frac{1}{[x]} \right]$, where $[x]$ denotes the greatest integer less than or equal to $x$, which of the following statements is true?

The range of the function $f(x) = [x] - x$ is

The set of all values of $x$ and the set of all values of $a$ for which the real-valued function $f(x) = \sqrt{\log_a(x - [x])}$ is defined are respectively: