Câu hỏi:
Cho hàm số với x là biến số, m là tham số. Khẳng định nào sau đây là đúng?
B. Nếu m > 0 thì hàm số nghịch biến trên ℝ, nếu m < 0 thì hàm số đồng biến trên ℝ;
C. Với mọi m hàm số luôn đồng biến trên ℝ;
D. Với mọi m hàm số luôn nghịch biến trên ℝ.
Trả lời:
Đáp án đúng: C
Ta có hàm số $y = ax + b$ đồng biến trên $\mathbb{R}$ khi $a > 0$ và nghịch biến trên $\mathbb{R}$ khi $a < 0$.
Trong bài toán này, $a = \sqrt{m^2 + 2022}$. Vì $m^2 \geq 0$ với mọi $m$ nên $m^2 + 2022 \geq 2022 > 0$.
Do đó $\sqrt{m^2 + 2022} > 0$ với mọi $m$. Vậy hàm số luôn đồng biến trên $\mathbb{R}$ với mọi $m$.
Trong bài toán này, $a = \sqrt{m^2 + 2022}$. Vì $m^2 \geq 0$ với mọi $m$ nên $m^2 + 2022 \geq 2022 > 0$.
Do đó $\sqrt{m^2 + 2022} > 0$ với mọi $m$. Vậy hàm số luôn đồng biến trên $\mathbb{R}$ với mọi $m$.
Câu hỏi này thuộc đề thi trắc nghiệm dưới đây, bấm vào Bắt đầu thi để làm toàn bài
18/09/2025
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Câu hỏi liên quan
Lời giải:
Đáp án đúng: A
Ta xét hai trường hợp:
Vậy $x_o = 3$.
- Trường hợp 1: $x_o \le -3$. Khi đó, $f(x_o) = -2x_o + 1 = 5$. Giải phương trình này, ta được $x_o = -2$. Tuy nhiên, điều kiện là $x_o \le -3$, nên trường hợp này không thỏa mãn.
- Trường hợp 2: $x_o > -3$. Khi đó, $f(x_o) = \frac{x_o + 7}{2} = 5$. Giải phương trình này, ta được $x_o + 7 = 10$, suy ra $x_o = 3$. Vì $3 > -3$, nên trường hợp này thỏa mãn.
Vậy $x_o = 3$.
Lời giải:
Đáp án đúng: A
Để tìm đáp án đúng, ta cần tính giá trị của hàm số $f(x)$ tại một số điểm và so sánh với các đáp án được đưa ra.
Xét $x=-1$, ta có $f(-1) = \frac{\sqrt[3]{2+3(-1)}}{-1-2} = \frac{\sqrt[3]{-1}}{-3}$.
Xét $x=3$, ta có $f(3) = \frac{2(3)+3}{3+1} = \frac{9}{4}$.
Vậy đáp án D đúng.
Xét $x=-1$, ta có $f(-1) = \frac{\sqrt[3]{2+3(-1)}}{-1-2} = \frac{\sqrt[3]{-1}}{-3}$.
Xét $x=3$, ta có $f(3) = \frac{2(3)+3}{3+1} = \frac{9}{4}$.
Vậy đáp án D đúng.
![Cho hàm số y = f(x) có tập xác định là [‒3; 3] và có đồ thị hàm số như hình vẽ. (ảnh 1)](data:image/png;base64,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)
