ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 177

\[1)\ f(x) = \frac{2x + 3}{x - 2}\]

\[x = \frac{2g(x) + 3}{g(x) - 2}\]

\[x \bullet g(x) - 2x = 2g(x) + 3\]

\[g(x) \bullet (x - 2) = 3 + 2x\]

\[g(x) = \frac{2x + 3}{x - 2};\]

\[g^{'}(x) = \frac{2(x - 2) - (2x + 3)}{(x - 2)^{2}}\]

\[g^{'}(x) = \frac{2x - 4 - 2x - 3}{(x - 2)^{2}}\]

\[g^{'}(x) = - \frac{7}{(x - 2)^{2}}.\]

\[2)\ f(x) = x^{2};\ \ x > 0:\]

\[x = g^{2}(x);\]

\[g(x) = \sqrt{x};\]

\[g^{'}(x) = \left( \sqrt{x} \right)^{'} = \frac{1}{2\sqrt{x}}.\]