Value of $$c$$ satisfying the conditions and conclusions of Rolle's theorem for the function $$\mathrm{f}(x)=x \sqrt{x+6}, x \in[-6,0]$$ is

If $$\mathrm{f}(x)=x \mathrm{e}^{x(1-x)}, x \in \mathrm{R}$$, then $$\mathrm{f}(x)$$ is

The value of $$\mathrm{c}$$ for the function $$\mathrm{f}(x)=\log x$$ on [$$1$$, e] if LMVT can be applied, is

Let $$\mathrm{f}(x)=\mathrm{e}^x-x$$ and $$\mathrm{g}(x)=x^2-x, \forall x \in \mathrm{R}$$, then the set of all $$x \in \mathrm{R}$$, where the function $$\mathrm{h}(x)=(\mathrm{fog})(x)$$ is increasing is