\(y=\sqrt{3+\cos x}-1\)
Do \(-1\le\cos x\le 1\)
\(\Rightarrow 3-1\le3+\cos x\le 1+3\)
\(\Rightarrow \sqrt{3-1}\le\sqrt{3+\cos x}\le \sqrt{1+3}\)
\(\Rightarrow \sqrt{3-1}-1\le\sqrt{3+\cos x}-1\le \sqrt{1+3}-1\)
\(\Rightarrow \sqrt{2}-1\le\sqrt{3+\cos x}-1\le \sqrt{4}-1\)
\(\Rightarrow \sqrt{2}-1\le y\le 1\)
Vậy hàm số đạt GTLN bằng \(1\) khi \(\cos x=1\);
đạt GTNN bằng \(\sqrt2-1\) khi \(\cos x=-1\).
