For a real number ' $a$ ', if a real valued function $f(x)=4 x^3+a x^2+3 x-2$ is monotonic in its domain, then the range of ' $a$ ' is

If $D \subseteq R$ and $f: D \rightarrow R$ defined by $f(x)=\frac{x^2+x+a}{x^2-x+a}$ is a surjection, then ' $a$ ' lies in the interval.

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