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Giải bài 79 trang 53 sách bài tập toán 11 - Cánh diều

Hàm số nào sau đây đồng biến trên tập xác định của nó?

😼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

Hàm số nào sau đây đồng biến trên tập xác định của nó?

A. \(y = {\left( {\frac{e}{\pi }} \right)^x}.\)

B. \(y = {\left( {\sqrt 3 } \right)^x}.\)

C. \(y = {\log _{0,3}}x.\)

D. \(y =  - {\log _2}x.\)

Phương pháp giải - Xem chi tiết

Hàm số mũ \(y = {a^x}\left( {0 < a < 1} \right)\) nghịch biến trên \(\mathbb{R}.\) Hàm số mũ \(y = {a^x}\left( {a > 1} \right)\) đồng biến trên \(\mathbb{R}.\)

Tập xác định của hàm số lôgarit \(y = {\log _a}x\left( {a > 0,a \ne 1} \right)\) là \(\left( {0; + \infty } \right).\)

Hàm số lôgarit \(y = {\log _a}x\) với \(a > 1\) đồng biến trên \(\left( {0; + \infty } \right).\) Hàm số lôgarit \(y = {\log _a}x\) với \(0 < a < 1\) nghịch biến trên \(\left( {0; + \infty } \right).\)

Lời giải chi tiết

Hàm số mũ \(y = {\left( {\sqrt 3 } \right)^x}\) đồng biến trên \(\mathbb{R}.\)

Ba hàm số còn lại đều nghịch biến trên tập xác định của nó.

Chọn đáp án B.

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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