Решебник по алгебре 11 класс Никольский Параграф 1. Функции и их графики Задание 9

\[\boxed{\mathbf{9.}}\]

\[\textbf{а)}\ y = \log_{2}|x|\]

\[|x| > 0\]

\[x \neq 0\]

\[D(f) = ( - \infty;0) \cup (0; + \infty)\text{.\ }\]

\[\textbf{б)}\ y = \left| \log_{2}x \right|\]

\[x > 0\]

\[D(f) = (0; + \infty).\]

\[\textbf{в)}\ y = \log_{2}\left( \text{tgx} \right)\]

\[tg\ x > 0\]

\[\pi k < x < \frac{\pi}{2} + \pi k;k \in Z.\]

\[D(f) = \left( \pi k;\frac{\pi}{2} + \pi k \right);k \in Z.\]

\[\textbf{г)}\ y = 2^{\sqrt{x}}\]

\[x \geq 0\]

\[D(f) = \lbrack 0; + \infty).\]

\[\textbf{д)}\ y = \sqrt{2^{x}}\]

\[2^{x} \geq 0\]

\[D(f) = R.\]

\[\textbf{е)}\ y = \sqrt{x^{2} - 1\ } + \sqrt{1 - x^{2}}\]

\[x^{2} - 1 \geq 0\]

\[(x + 1)(x - 1) \geq 0\]

\[x \leq - 1;\ \ x \geq 1.\]

\[1 - x^{2} \geq 0\]

\[x^{2} - 1 \leq 0.\]

\[(x + 1)(x - 1) \leq 0\]

\[- 1 \leq x \leq 1.\]

\[D(f) = \left\{ - 1 \right\};\left\{ 1 \right\}.\]