Mathematics - Functions Question with Solution | TestHub

$\mathrm{f}(\mathrm{x})=\Rightarrow |\mathrm{x}\ln \mathrm{x}|$

Graph of f(x):

Obviously least value

Ocurs at $\mathrm{x}=\mathrm{e}$

$\therefore \mathrm{m}=|\mathrm{e}|\mathrm{ne}\mid =\mathrm{e}$.

$\therefore {\mathrm{e}}^{|{\mathrm{x}}^2-4\mathrm{x}+5|}={\mathrm{e}}^1$

$\Rightarrow {\mathrm{x}}^2-4\mathrm{x}+4=0$ and ${\mathrm{x}}^2-4\mathrm{x}+6=0$

$\Rightarrow \mathrm{x}=2$ and no solution But $x=2\notin [e,\infty )$

⇒ No value of x is possible.