Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 171

\[1)\ f(y) = y^{2};y = g(x) = x + 1:\]

\[f\left( g(x) \right) = (x + 1)^{2};\]

\[D(x) = R;\]

\[E(y) = \lbrack 0;\ + \infty).\]

\[2)\ f(y) = \lg y;y = g(x) = \sqrt{x - 1}:\]

\[f\left( g(x) \right) = \lg\sqrt{x - 1};\]

\[D(x) = (1;\ + \infty);\]

\[E(y) = R.\]

\[3)\ f(y) = \frac{y + 1}{y - 2};y = g(x) = \log_{2}x:\]

\[f\left( g(x) \right) = \frac{\log_{2}x + 1}{\log_{2}x - 2};\]

\[D(x) = (0;\ 4) \cup (4;\ + \infty);\ \ \]

\[E(y) = ( - \infty;\ 1) \cup (1;\ + \infty).\]

\[4)\ f(y) = \sqrt{y};\ y = g(x) = \frac{x + 2}{x - 3}:\]

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

\[D(x) = ( - \infty;\ - 2\rbrack \cup (3;\ + \infty);\]

\[E(y) = \lbrack 0;\ 1) \cup (1;\ + \infty).\]