\(f\left(x\right)>0,\forall x\in R\Leftrightarrow\left\{{}\begin{matrix}a>0\\\Delta< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m+1>0\\\left[-2\left(m-1\right)\right]^2-4\left(m+1\right)\left(-m+4\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>-1\\4\left(m^2-2m+1\right)-4\left(-m^2+4m-m+4\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow4m^2-8m+4+4m^2-12m-16< 0\)
\(\Leftrightarrow8m^2-20m-12< 0\)
\(KL:m\in\left(-1;3\right)\)