Answer
$$|f(1) - f(0)| - [g(1)]^{2} + g(1) \div f(-1) \cdot g(2)=0$$
Work Step by Step
$$|f(1) - f(0)| - [g(1)]^{2} + g(1) \div f(-1) \cdot g(2)$$
The values of $f(1), f(0), g(1), f(-1), g(2)$ can be obtained from the given table. The values in the parentheses indicate the value of $f$ or a given value of $x$.
Based on the table:
$f(1) = -4$
$f(0) = -1$
$g(1) = -3$
$f(-1) = 3$
$g(2) = -6$
Plugging these values to the original equation:
$$=|-4 - (-1)| - [-3]^{2} + (-3) \div 3 \cdot -6$$ $$=|-3| - 9 + (-3) \div 3 \cdot -6$$ $$=3 - 9 + (-1) \cdot -6$$ $$=3 - 9 + 6$$ $$=0$$
