Domain of $f(x) = \frac{x}{1-|x|}$ is

If the real valued function $f(x)=\sin ^{-1}(x^2-1)-3 \log _3(3^x-2)$ is not defined for all $x \in(-\infty, a] \cup(b, \infty)$, then $3^a+b^2=$

The domain and range of the relation $R$ given by $R = \{(x, y) : y = x + \frac{6}{x}, x, y \in N \text{ and } x < 6\}$ are

The domain of $\sqrt{|x|-x}$ is

The range of the function $f(x)=\sin [x]$,where $-\frac{\pi}{4} < x < \frac{\pi}{4}$ and $[x]$ denotes the greatest integer $\leq x$,is

The range of the polynomial $P(x) = 4x^3 - 3x$ as $x$ varies over the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is