Giải thích các bước giải:
$e.f(x)=\cos x-\sqrt{3}\sin x$
$\to \dfrac 12 f(x)=\dfrac 12\cos x-\dfrac{\sqrt{3}}{2}\sin x$
$\to \dfrac 12 f(x)=\cos\dfrac{\pi}{3}\cos x-\sin x\sin\dfrac{\pi}{3}$
$\to \dfrac 12 f(x)=\cos (x+\dfrac{\pi}{3})$
$\to -1\le \dfrac 12f(x)\le 1$
$\to -2\le f(x)\le 2$
$f.y=\sqrt{5+\sin x-\cos x}$
$\to y=\sqrt{5+\sqrt{2}.(\dfrac{1}{\sqrt{2}}\sin x-\dfrac{1}{\sqrt{2}}\cos x)}$
$\to y=\sqrt{5+\sqrt{2}.\sin(x- \dfrac{\pi}{4})}$
$\to \sqrt{5+\sqrt{2}.-1}\le y=\sqrt{5+\sqrt{2}.\sin(x- \dfrac{\pi}{4})}\le \sqrt{5+\sqrt{2}.1}$
$\to \sqrt{5-\sqrt{2}}\le y\le \sqrt{5+\sqrt{2}}$