2: \(0< =cos^2x< =1\)
=>\(0< =3\cdot cos^2x< =3\)
=>\(0+7< =3cos^2x+7< =3+7\)
=>7<=y<=10
Vậy: TGT là T=[7;10]
3: \(-1< =-\sqrt{sinx}< =0\)
=>\(-4< =-4\sqrt{sinx}< =0\)
=>\(-4+6< =-4\sqrt{sinx}+6< =0+6\)
=>2<=y<=6
\(y_{min}=2\) khi sin x=1
=>\(x=\dfrac{\Omega}{2}+k2\Omega\)
\(y_{max}=6\) khi sin x=0
=>\(x=k\Omega\)
3) \(y=-4\sqrt{sinx}+6\)
Ta có : \(-1\le sinx\le1\)
\(\Leftrightarrow0\le\sqrt{sinx}\le1\)
\(\Leftrightarrow-4\le-4\sqrt{sinx}\le0\)
\(\Leftrightarrow2\le y=-4\sqrt{sinx}+6\le6\)
\(\Rightarrow GTNN\left(y\right)=2\left(x=\dfrac{\pi}{2}+k2\pi\right);\left(k\in Z\right)\)
\(GTLN\left(y\right)=6\left(x=k\pi\right);\left(k\in Z\right)\)
Câu 2
Ta có:\(-1\le\cos x\le1\)
\(\Rightarrow0\le\cos^2x\le1\Rightarrow0\le3\cos^2x\le3\)
\(\Rightarrow7\le3\cos^2x+7\le10\)
Hay \(7\le y\le10\)
Vậy ....
