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Find the number of negative integral values of $m$ for which the expression $x^{2}+2\left( m-1 \right)x+m+5$ is positive $\forall$ $x \gt 1$.

A function $f:R\to R$ is defined as $f\left( x \right)=3x+5$. Find $f^{-1}\left( x \right)$.

Let $f:R\to \left( 0,\infty \right)$ be such that $f\left( x \right)+\frac{e^{x+x^{2}}}{f\left( x \right)}\le e^{x}+e^{x^{2}}, \forall$ $x>0$. Then, $\displaystyle\lim_{x \to 1} f\left( x \right)$ is