Question

помогите найти облость определения

Answer 1

Подкоренное выражение неотрицательно, знаменатель не равен 0

$\sqrt{\frac{5}{x^2-9}} \geq 0$
$x^2-9 \neq 0$
$x-4 \neq 0$

$x^2-9 > 0$
$x \neq 4$

$x^2 > 9$
$x \neq 4$

$x^2 > 3^2$
$x \neq 4$

$|x| > 3$
$x \neq 4$

$x < -3$ или $x > 3$
$x \neq 4$

откуда обьединяя
$D(y)=(-\infty;-3) \cup(3;4) \cup (4;+\infty)$

Answer 2

Х^2-9 должно быть строго больше нуля (подкоренное выражение должно быть положительно, и на 0 делить нельзя.
Раскладывая на множители имеем 2 корня : 3 и -3.
область определения  от - бесконечности до -3, и от +3 до плюс бесконечности.
Но х-4 не должно быть равно 0 т.е. х не равен 4
Имеем 3 промежутка : от - бесконечности  до -3, от 3 до 4 и от 4 до + бесконечности.  Все точки -3, +3и +4  выколоты. Скобки круглые.

Answer 3

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