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sinusoida2000
@sinusoida2000
August 2022
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ПОЖАЛУЙСТА,ПОМОГИТЕ НАЙТИ ОБЛАСТЬ ОПРЕДЕЛЕНИЯ И ОБЛАСТЬ ЗНАЧЕНИЯ ФУНКЦИИ:
y=(cosx-1)^(1/2)+1
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ruinfo777
НАЙТИ ОБЛАСТЬ ОПРЕДЕЛЕНИЯ И ОБЛАСТЬ ЗНАЧЕНИЯ ФУНКЦИИ:
y=(cosx-1)^(1/2)+1
-------
y=√(cosx-1)+1 =1 +√-(1 -cosx) =1 +√(-2sin²x/2) =1 +
√2 *√(-sin²x/2) ;
ООФ :
-sin²x/2 ≥ 0 ⇔ sin²x/2≤ 0
⇔
sinx/2 =0
⇔x/2 =πn , n∈Z
⇔x =
2πn , n∈Z.
Область Значения Функции : E(y) = 1 +
√2 *√(-sin²x/2) =1
* * *
sinx/2 =0 * * *
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Answers & Comments
y=(cosx-1)^(1/2)+1
-------
y=√(cosx-1)+1 =1 +√-(1 -cosx) =1 +√(-2sin²x/2) =1 +√2 *√(-sin²x/2) ;
ООФ : -sin²x/2 ≥ 0 ⇔ sin²x/2≤ 0 ⇔ sinx/2 =0 ⇔x/2 =πn , n∈Z ⇔x =2πn , n∈Z.
Область Значения Функции : E(y) = 1 +√2 *√(-sin²x/2) =1 * * * sinx/2 =0 * * *