Question

Решите уравнение пожалуйста (21)

Answer 1

$f\left ( x \right )=e^{x+\frac{1}{x}}\Leftrightarrow lnf\left ( x \right )=x+\frac{1}{x}\\\frac{1}{f\left ( x \right )}\cdot f'\left ( x \right )=1-\frac{1}{x^2}\Leftrightarrow f'\left ( x \right )=\left ( 1-\frac{1}{x^2} \right )e^{x+\frac{1}{x}}\\f'\left ( x \right )=0\Rightarrow x\pm 1\\f\left ( 1 \right )=e^2\\f\left ( -1 \right )=e^{-2}\\E_f=\left ( 0;e^{-2} \right ]\cup \left [ e^2;+\infty \right )$