If the domain of the real valued function $f(x)=\frac{1}{\sqrt{\log _{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a, b)$, then $2 b=$

A real valued function $f:[4, \infty) \rightarrow R$ is defined as $f(x)=\left(x^2+x+1\right)^{\left(x^2-3 x-4\right)}$, then $f$ is

If $f: R-\{0\} \rightarrow R$ is defined by $3 f(x)+4 f\left(\frac{1}{x}\right)=\frac{2-x}{x}$ then $f(3)=$

The inverse of the function $y=\frac{10^x-10^{-x}}{10^x+10^{-x}}+1$ is $x=$