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Bài 1.20 trang 30 SGK Toán 11 tập 1 - Cùng khám phá

Tìm tập xác định của các hàm số:
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Đề bài

Tìm tập xác định của các hàm số: a) \(y = \frac{{1 + \sin x}}{{\cos x}};\) b) \(y = \sqrt {\frac{{1 + \cos x}}{{2 - \sin x}}} .\)

Phương pháp giải - Xem chi tiết

Hàm phân thức xác định khi mẫu khác 0. Hàm chứa căn xác định khi biểu thức trong căn lớn hơn hoặc bằng 0.

Lời giải chi tiết

a) Hàm số xác định \( \Leftrightarrow \cos x \ne 0 \Leftrightarrow x \ne \frac{\pi }{2} + k2\pi ,k \in \mathbb{Z}\)Vậy \(D = \mathbb{R}\backslash \left\{ {\frac{\pi }{2} + k2\pi ,k \in \mathbb{Z}} \right\}\)b) Hàm số xác định \( \Leftrightarrow \frac{{1 + \cos x}}{{2 - \sin x}} \ge 0\)Mà \(\cos x \ge  - 1 \Leftrightarrow 1 + \cos x \ge 1 > 0\forall x\)\(\sin x \le 1 \Leftrightarrow  - \sin x \ge  - 1 \Leftrightarrow 2 - \sin x \ge 1 > 0\forall x\)\( \Rightarrow \frac{{1 + \cos x}}{{2 - \sin x}} > 0\forall x\)Vậy \(D = \mathbb{R}\)

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