Answer
The value of the given expression is $-38$
Work Step by Step
Substitute the value of the functions as given in the table to obtain the following expression
$\begin{align}
& \sqrt{f\left( -1 \right)-f\left( 0 \right)}-{{\left[ g\left( 2 \right) \right]}^{2}}+f\left( -2 \right)\div g\left( 2 \right)\cdot g\left( -1 \right)=\sqrt{3-\left( -1 \right)}-{{\left[ -6 \right]}^{2}}+6\div \left( -6 \right)\cdot 4 \\
& =\sqrt{4}-36+\left( -1 \right)\cdot 4 \\
& =2-36-4 \\
& =-38
\end{align}$
Therefore, the value of the expression is:
$\sqrt{f\left( -1 \right)-f\left( 0 \right)}-{{\left[ g\left( 2 \right) \right]}^{2}}+f\left( -2 \right)\div g\left( 2 \right)\cdot g\left( -1 \right)=-38$.
