Tìm GTLN GTNN của hàm số y=căn2 sin(x\2-pi\4)-1

$\begin{array}{l} - 1 \le \sin \left( {\frac{x}{2} - \frac{\pi }{4}} \right) \le 1 \Rightarrow - \sqrt 2 \le \sqrt 2 \sin \left( {\frac{x}{2} - \frac{\pi }{4}} \right) \le \sqrt 2 \\ \Rightarrow - \sqrt 2 - 1 \le \sqrt 2 \sin \left( {\frac{x}{2} - \frac{\pi }{4}} \right) - 1 \le \sqrt 2 - 1 \end{array}$ $\begin{array}{l} \Rightarrow \min y = - \sqrt 2 - 1\,khi\,\\ \sin \left( {\frac{x}{2} - \frac{\pi }{4}} \right) = - 1 \Leftrightarrow \frac{x}{2} - \frac{\pi }{4} = - \frac{\pi }{2} + k2\pi \Leftrightarrow x = - \frac{\pi }{2} + k4\pi \\ \Rightarrow \max y = \sqrt 2 - 1\,khi\,\\ \sin \left( {\frac{x}{2} - \frac{\pi }{4}} \right) = 1 \Leftrightarrow \frac{x}{2} - \frac{\pi }{4} = \frac{\pi }{2} + k2\pi \Leftrightarrow x = \frac{{3\pi }}{2} + k4\pi \end{array}$