Domain of the real valued function $f(x) = \log(x^2 - 1) + x \operatorname{coth}^{-1} x$ is

If $[x]^2-5[x]+6=0$,where $[.]$ denotes the greatest integer function,then

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 $k=$

If the domain of the function $f(x) = \sqrt{\ln(m\sin x + 4)}$ is $R$,then the number of possible integral values of $m$ is:

If $D$ is the domain and $G$ is the range of the real-valued function $f(x)=\sqrt{\frac{1-x^2}{1+x^2}}$, then $D \cap G=$

$f(x)$ is a quadratic polynomial satisfying the condition $f(x) + f\left(\frac{1}{x}\right) = f(x) f\left(\frac{1}{x}\right)$. If $f(-1) = 0$,then the range of $f$ is