a) \(F=2\left|3x-2\right|-1\)
Vì \(\left|3x-2\right|\ge0\forall x\Rightarrow2\left|3x-2\right|\ge0\)
\(\Rightarrow2\left|3x-2\right|-1\ge-1\)
''='' xảy ra khi \(3x-2=0\Rightarrow x=\dfrac{2}{3}\)
=> \(F_{min}=-1\)
b) \(G=x^2+3\left|y-2\right|-1\)
Ta có: \(\left\{{}\begin{matrix}x^2\ge0\forall x\\3\left|y-2\right|\ge0\forall y\end{matrix}\right.\)
=> \(x^2+3\left|y-2\right|\ge0\Rightarrow x^2+3\left|y-2\right|-1\ge-1\)
''='' xảy ra khi \(\left\{{}\begin{matrix}x^2=0\\y-2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\y=2\end{matrix}\right.\)
Vậy \(G_{min}=-1\)
\(A=2\left|3x-2\right|-1\ge-1\)
Dấu "=" xảy ra khi : \(x=\dfrac{2}{3}\)
\(B=x^2+3\left|y-2\right|-1\ge-1\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}x=0\\y=2\end{matrix}\right.\)