Задача 71194 Найти область опредепения функции f(x) =...

63f257933348577249b52495

04.05.2023 08:30:33

Найти область опредепения функции f(x) = arccos (x-8)/(x-24)

5f3ea7e3faf909182968ddd9

04.05.2023 08:53:24

★

[m]-1 ≤ \frac{x-8}{x-24} ≤ 1[/m]

[m]\left\{\begin {matrix} \frac{x-8}{x-24} ≤ 1\\ \frac{x-8}{x-24} ≥ - 1\end {matrix}\right.[/m]


[m]\left\{\begin {matrix} \frac{x-8}{x-24} -1≤ 0\\ \frac{x-8}{x-24} +1 ≥ 0\end {matrix}\right.[/m]

[m]\left\{\begin {matrix} \frac{x-8-x+24}{x-24} ≤ 0\\ \frac{x-8+x-24}{x-24} ≥ 0\end {matrix}\right.[/m]

[m]\left\{\begin {matrix} \frac{16}{x-24} ≤ 0\\ \frac{2x-32}{x-24} ≥ 0\end {matrix}\right.[/m]

[m]\left\{\begin {matrix} x-24 < 0\\ 2x-32 ≤ 0\end {matrix}\right.[/m]

[m]\left\{\begin {matrix} x < 24 \\ x ≤ 16\end {matrix}\right.[/m]

О т в е т. (- ∞ ; 16]