Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 92

\[1)\ y = tg\ x \bullet ctg\ x = 1\]

\[x \neq \frac{\pi}{2} + \pi n\]

\[x \neq \pi n.\]

\[2)\ y = \sin x \bullet ctg\ x = \cos x\]

\[x \neq \pi n.\]

\[3)\ y = 2^{\text{tg\ x}}\]

\[tg\ x = 0:\]

\[y = 2^{0} = 1.\]

\[\text{tg\ x} = 1:\]

\[y = 2^{1} = 2.\]

\[\text{tg\ x} > 1:\]

\[2^{\text{tg\ x}} > 2^{1}\]

\[\text{\ y} > 2.\]

\[\text{tg\ x} < 1:\]

\[2^{- \infty} < 2^{\text{tg\ x}} < 2^{1}\]

\[0 < y < 1.\]

\[4)\ y = \sqrt{\text{ctg\ x}}\]

\[ctg\ x = 0:\]

\[y = \sqrt{0} = 0.\]

\[ctg\ x = 1:\]

\[y = \sqrt{1} = 1.\]

\[\text{ctg\ x} > 1:\]

\[\sqrt{\text{ctg\ x}} > \sqrt{1}\]

\[\text{\ y} > 1.\]

\[Область\ определения:\]

\[ctg\ x \geq 0.\]