Toán Lớp 11: y=cos²x-cosx+2
Tìm tập giá trị T
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Toán Lớp 11: y=cos²x-cosx+2
Tìm tập giá trị T
Comments ( 1 )
y = {\cos ^2}x – \cos x + 2\\
= {\cos ^2}x – 2.\cos x.\dfrac{1}{2} + \dfrac{1}{4} + \dfrac{7}{4}\\
= {\left( {\cos x – \dfrac{1}{2}} \right)^2} + \dfrac{7}{4}\\
Do: – 1 \le \cos x \le 1\\
\Leftrightarrow – 1 – \dfrac{1}{2} \le \cos x – \dfrac{1}{2} \le 1 – \dfrac{1}{2}\\
\Leftrightarrow – \dfrac{3}{2} \le \cos x – \dfrac{1}{2} \le \dfrac{1}{2}\\
\Leftrightarrow 0 \le {\left( {\cos x – \dfrac{1}{2}} \right)^2} \le \dfrac{9}{4}\\
\Leftrightarrow \dfrac{7}{4} \le {\left( {\cos x – \dfrac{1}{2}} \right)^2} + \dfrac{7}{4} \le 4\\
\Leftrightarrow \dfrac{7}{4} \le y \le 4\\
\Leftrightarrow TGT:T = \left[ {\dfrac{7}{4};4} \right]
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