Đáp án:
Giải thích các bước giải:
$a)y=2sin(x+\dfrac{\pi}{4})+1$
Ta có:$-1≤sin (x+ \dfrac{\pi}{4})≤1\\\Leftrightarrow -2 ≤2sin(x+\dfrac{\pi}{4})≤2\\\Leftrightarrow-1≤2sin(x+\dfrac{\pi}{4})+1≤3\\\rightarrow Miny= -1\\\rightarrow Maxy =3$
$b) y =2\sqrt{cosx+1}+3$
Ta có:$-1≤cosx≤1\\\Leftrightarrow 0 ≤cosx+1≤2\\\Leftrightarrow0 ≤\sqrt{cosx+1}≤\sqrt{2}\\\Leftrightarrow 0≤2\sqrt{cosx+1}≤2\sqrt{2}\\\Leftrightarrow-3≤2\sqrt{cosx+1}-3≤2\sqrt{2}-3\\\rightarrow Miny=-3\\\rightarrow Mayx=2\sqrt{2}-3$
$c)y=4sin^2x-4sinx+3=(2sin^2x)-2.2sinx .1 +1^2 +2=(2sinx-1)^2+2$
Ta có:$-1\leq sinx \leq 1 \\\Leftrightarrow -2 \leq 2sinx \leq 2\\\Leftrightarrow -3 \leq 2sinx -1 \leq 1\\\Leftrightarrow 9\geq (2sinx-1)^2 \geq 1\\\Leftrightarrow 11 \geq (2sinx -1)^2 +2 \geq 3 \\\rightarrow Miny =3\\\rightarrow Mayx =11$
