Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 756

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\[1)\ y = \arcsin\frac{x - 3}{2}\]

\[- 1 \leq \frac{x - 3}{2} \leq 1\]

\[- 2 \leq x - 3 \leq 2\]

\[1 \leq x \leq 5.\]

\[Ответ:\ \ x \in \lbrack 1;\ 5\rbrack.\]

\[2)\ y = \arccos(2 - 3x)\]

\[- 1 \leq 2 - 3x \leq 1\]

\[- 3 \leq - 3x \leq - 1\]

\[\frac{1}{3} \leq x \leq 1.\]

\[Ответ:\ \ x \in \left\lbrack \frac{1}{3};\ 1 \right\rbrack.\]

\[3)\ y = \arccos\left( 2\sqrt{x} - 3 \right)\]

\[- 1 \leq 2\sqrt{x} - 3 \leq 1\]

\[2 \leq 2\sqrt{x} \leq 4\]

\[1 \leq \sqrt{x} \leq 2\]

\[1 \leq x \leq 4.\]

\[Ответ:\ \ x \in \lbrack 1;\ 4\rbrack.\]

\[4)\ y = \arcsin\left( \frac{2x^{2} - 5}{3} \right)\]

\[- 1 \leq \frac{2x^{2} - 5}{3} \leq 1\]

\[- 3 \leq 2x^{2} - 5 \leq 3\]

\[2 \leq 2x^{2} \leq 8\]

\[1 \leq x^{2} \leq 4\]

\[\left\{ \begin{matrix} - 2 \leq x \leq - 1 \\ 1 \leq x \leq 2\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\(Ответ:\ \ x \in \lbrack - 2;\ - 1\rbrack \cup \lbrack 1;\ 2\rbrack.\)