$\begin{array}{l}
y = 2{\cos ^2}x - 1\\
- 1 \le \cos x \le 1 \Rightarrow 0 \le {\cos ^2}x \le 1\\
\Rightarrow - 1 \le y \le 2 \Rightarrow \left\{ \begin{array}{l}
\min y = 0\\
\max y = 1
\end{array} \right.\\
y = \sqrt {2\sin x + 3} \\
- 1 \le \sin x \le 1 \Rightarrow - 2 \le 2\sin x \le 2 \Rightarrow 1 \le 2\sin x + 3 \le 5\\
\Rightarrow 1 \le y \le \sqrt 5 \Rightarrow \left\{ \begin{array}{l}
\max y = \sqrt 5 \\
\min y = 1
\end{array} \right.
\end{array}$
