1.
\(sin\left(x-\dfrac{\pi}{3}\right)\in\left[-1;1\right]\)
\(\Rightarrow y=2sin\left(x-\dfrac{\pi}{3}\right)+3\in\left[1;5\right]\)
\(\Rightarrow\left\{{}\begin{matrix}y_{min}=1\\y_{max}=5\end{matrix}\right.\)
2.
\(cos2x\in\left[-1;1\right]\)
\(\Rightarrow y=3-\dfrac{1}{2}cos2x\in\left[\dfrac{5}{2};\dfrac{7}{2}\right]\)
\(\Rightarrow\left\{{}\begin{matrix}y_{min}=\dfrac{5}{2}\\y_{max}=\dfrac{7}{2}\end{matrix}\right.\)
3.
\(y=\dfrac{1+3cos^2x}{2}=\dfrac{\dfrac{3}{2}\left(2cos^2x-1\right)+\dfrac{5}{2}}{2}=\dfrac{3}{4}cos2x+\dfrac{5}{4}\)
Vì \(cos2x\in\left[-1;1\right]\Rightarrow y=\dfrac{3}{4}cos2x+\dfrac{5}{4}\in\left[\dfrac{1}{2};2\right]\)
\(\Rightarrow\left\{{}\begin{matrix}y_{min}=\dfrac{1}{2}\\y_{max}=2\end{matrix}\right.\)
