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sustention
@sustention
August 2022
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Найдите область определения (задание прикреплено) .
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oganesbagoyan
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Task/28840008
-------------------
Найди область определения √ (x² + x -2)
/
(x² - 4) .
--------------- решение :
( x² + x -2) / (x² - 4) ≥ 0 ⇔ ( x +2)(x-1)
/
(x + 2) (x -2) ≥ 0 ⇔
{ x≠ - 2 , { x≠ ± 2 ,
{ (x-1)
/
(x - 2) ≥ 0 . {(x-1)*(x - 2) ≥ 0 . методом интервалов
" +" " +" " -" "+"
//////////////////////// (-2) //////////////////// [1] ---------------- (2) /////////////////////
ответ: x ∈ (- ∞ ; -2) ∪ ( -2 ; 1] ∪ (2 ; ∞).
2 votes
Thanks 1
sustention
а можете объяснить, почему на (- ∞;-2) + ?
oganesbagoyan
-2 ∉ ОДЗ
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Answers & Comments
Verified answer
Task/28840008-------------------
Найди область определения √ (x² + x -2) / (x² - 4) .
--------------- решение :
( x² + x -2) / (x² - 4) ≥ 0 ⇔ ( x +2)(x-1) / (x + 2) (x -2) ≥ 0 ⇔
{ x≠ - 2 , { x≠ ± 2 ,
{ (x-1) / (x - 2) ≥ 0 . {(x-1)*(x - 2) ≥ 0 . методом интервалов
" +" " +" " -" "+"
//////////////////////// (-2) //////////////////// [1] ---------------- (2) /////////////////////
ответ: x ∈ (- ∞ ; -2) ∪ ( -2 ; 1] ∪ (2 ; ∞).