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Giải bài 31 trang 21 sách bài tập toán 11 - Cánh diều

Tập xác định của hàm số (y = sqrt {1 + cos 2x} ) là:

🔴Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Tập xác định của hàm số \(y = \sqrt {1 + \cos 2x} \) là: A. \(\emptyset \)                      B. \(\mathbb{R}\)                             C. \(\left[ { - 1; + \infty } \right)\)                D. \(\left[ { - \frac{1}{2}; + \infty } \right)\)

Phương pháp giải - Xem chi tiết

Hàm số xác định khi \(1 + \cos 2x \ge 0\)

Xác định miền giá trị của biểu thức \(1 + \cos 2x\) và kết luận.

Lời giải chi tiết

Biểu thức \(y = \sqrt {1 + \cos 2x} \) có nghĩa khi \(1 + \cos 2x \ge 0\).

Do với \(\forall x \in \mathbb{R}\), ta có \(\cos 2x \ge  - 1 \Rightarrow 1 + \cos 2x \ge 0\).

Như vậy hàm số \(y = \sqrt {1 + \cos 2x} \) có tập xác định là \(\mathbb{R}\).

Đáp án đúng là B.

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