Answer
The value of expression is 0.
Work Step by Step
Consider the given expression:
$\left| f\left( 1 \right)-f\left( 0 \right) \right|-{{\left[ g\left( 1 \right) \right]}^{2}}+g\left( 1 \right)\div f\left( -1 \right)\cdot g\left( 2 \right)$
Put the values of the functions as given in the table to obtain the following expression:
$\begin{align}
& \left| f\left( 1 \right)-f\left( 0 \right) \right|-{{\left[ g\left( 1 \right) \right]}^{2}}+g\left( 1 \right)\div f\left( -1 \right)\cdot g\left( 2 \right)=\left| -4-\left( -1 \right) \right|-{{\left[ -3 \right]}^{2}}+\left( -3 \right)\div 3\cdot \left( -6 \right) \\
& =\left| -3 \right|-9+\left( -1 \right)\cdot \left( -6 \right) \\
& =3-9+6 \\
& =0
\end{align}$
Therefore, the value of the expression $\left| f\left( 1 \right)-f\left( 0 \right) \right|-{{\left[ g\left( 1 \right) \right]}^{2}}+g\left( 1 \right)\div f\left( -1 \right)\cdot g\left( 2 \right)$ is $0$.
