Question

Tìm TXĐ của HSLG sau: \(y=3\cos2x-2\cos^2x+5\)

Answer 1

\(\Leftrightarrow y=3\cos2x-2\left(\dfrac{1+\cos2x}{2}\right)+5\)

\(\Leftrightarrow y=3\cos2x-1-\cos2x+5\)

\(\Leftrightarrow y=2\cos2x+4\)

\(Vì\) \(-1\le\cos2x\le1\)

\(\Rightarrow-2\le2\cos2x\le2\)

\(\Rightarrow2\le2\cos2x+4\le6\)

\(\Rightarrow2\le y\le6\)

\(Vậy\) \(y_{max}=6\)

        \(y_{min}=2\)