Найдите область определения выражения: f(x)=корень из (x-(8/(x-2)).

Ответ:

\[f(x) = \sqrt{x - \frac{8}{x - 2}}\]

\[x^{\backslash x - 2} - \frac{8}{x - 2} \geq 0;\ \ x \neq 2\]

\[\frac{x^{2} - 2x - 8}{x - 2} \geq 0\]

\[x^{2} - 2x - 8 = (x + 2)(x - 4)\]

\[D_{1} = 1 + 8 = 9\]

\[x_{1} = 1 + 3 = 4;\]

\[x_{2} = 1 - 3 = - 2;\]

\[\frac{(x + 2)(x - 4)}{x - 2} \geq 0\]

\[- 2 \leq x < 2;x \geq 4.\]

\[Ответ:\ - 2 \leq x < 2;x \geq 4.\]