Answer
See the explanation below.
Work Step by Step
(a)
Provided function $g\left( x \right)=3{{x}^{2}}-5x+2$.
To find $g\left( 0 \right)$, put $x=0$ in function $g\left( x \right)=3{{x}^{2}}-5x+2$.
$\begin{align}
& g\left( x \right)=3{{x}^{2}}-5x+2 \\
& g\left( 0 \right)=3{{\left( 0 \right)}^{2}}-5\left( 0 \right)+2 \\
& =2.
\end{align}$
(b)
Provided function $g\left( x \right)=3{{x}^{2}}-5x+2$.
To find $g\left( -2 \right)$, put $x=-2$ in function $g\left( x \right)=3{{x}^{2}}-5x+2$.
$\begin{align}
& g\left( x \right)=3{{x}^{2}}-5x+2 \\
& g\left( -2 \right)=3{{\left( -2 \right)}^{2}}-5\left( -2 \right)+2 \\
& =3\left( 4 \right)+10+2 \\
& =24.
\end{align}$
(c)
Provided function $g\left( x \right)=3{{x}^{2}}-5x+2$.
To find $g\left( x-1 \right),$ put $x=x-1$ in function $g\left( x \right)=3{{x}^{2}}-5x+2$.
$\begin{align}
& g\left( x-1 \right)=3{{\left( x-1 \right)}^{2}}-5\left( x-1 \right)+2 \\
& =3\left( {{x}^{2}}-2x+1 \right)-5x+5+2 \\
& =3{{x}^{2}}-6x+3-5x+7 \\
& =3{{x}^{2}}-11x+10
\end{align}$
(d)
Provided function $g\left( x \right)=3{{x}^{2}}-5x+2$.
To find $g\left( -x \right),$ put $x=-x$ in function $g\left( x \right)=3{{x}^{2}}-5x+2$.
$\begin{align}
& g\left( x \right)=3{{x}^{2}}-5x+2 \\
& g\left( -x \right)=3{{\left( -x \right)}^{2}}-5\left( -x \right)+2 \\
& =3{{x}^{2}}+5x+2
\end{align}$
