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Giải bài 6.13 trang 14 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Tìm tập xác định và tập giá trị của các hàm số bậc hai sau:

ꦗTổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Tìm tập xác định và tập giá trị của các hàm số bậc hai sau: a) \(f(x) =  - {x^2} + 4x - 3\)    b) \(f(x) = {x^2} - 7x + 12\)

Phương pháp giải - Xem chi tiết

Hàm số bậc hai \(y = a{x^2} + bx + c(a \ne 0)\) có tập xác định là \(\mathbb{R}\) và có tập giá trị là \(\left[ { - \frac{\Delta }{{4a}}; + \infty } \right)\) (Nếu a > 0) hoặc \(\left( { - \infty ; - \frac{\Delta }{{4a}}} \right]\) (Nếu a < 0)

Lời giải chi tiết

a) Hàm số \(f(x) =  - {x^2} + 4x - 3\) có tập xác định là D = \(\mathbb{R}\)

Do a⛦ = -1 < 0, ∆ = 4 nên hàm số \(f(x) =  - {x^2} + 4x - 3\) có tập giá trị là \(\left( { - \infty ;1} \right]\)

b) Hàm số \(f(x) = {x^2} - 7x + 12\) có tập xác định là D = \(\mathbb{R}\)

Do a🎶 = 1 > 0, ∆ = 1 nên hàm số \(f(x) = {x^2} - 7x + 12\)có tập giá trị là \(\left[ { - \frac{1}{4}; + \infty } \right)\)

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