Question

let f and g be defined by the table to the right. find the following.\\(\sqrt{f(-1) - f(0)} - g(2)^2 + f(-2) + g(2) \cdot g(-1)\\)\
\\(\

$$\begin{array}{|c|c|c|} \\hline x & f(x) & g(x) \\\\ \\hline -2 & 7 & 4 \\\\ \\hline -1 & 8 & 9 \\\\ \\hline 0 & -8 & 8 \\\\ \\hline 1 & -9 & -8 \\\\ \\hline 2 & -4 & -7 \\\\ \\hline \\end{array}$$

\\)\
\\(\sqrt{f(-1) - f(0)} - g(2)^2 + f(-2) + g(2) \cdot g(-1) = \boxed{}\\)\
(simplify your answer.)

Explanation:

Step1: Find values from the table

From the table:

• \( f(-1) = 8 \), \( f(0) = -8 \), \( g(2) = -7 \), \( f(-2) = 7 \), \( g(-1) = 9 \)

Step2: Substitute values into the expression

First, calculate \( f(-1) - f(0) \):
\( f(-1) - f(0) = 8 - (-8) = 16 \)

Then, \( \sqrt{f(-1) - f(0)} = \sqrt{16} = 4 \)

Next, \( [g(2)]^2 = (-7)^2 = 49 \)

Then, \( g(2) \cdot g(-1) = (-7) \cdot 9 = -63 \)

Now substitute all into the original expression:
\( \sqrt{f(-1) - f(0)} - [g(2)]^2 + f(-2) + g(2) \cdot g(-1) = 4 - 49 + 7 + (-63) \)

Step3: Simplify the arithmetic

Calculate step by step:
\( 4 - 49 = -45 \)
\( -45 + 7 = -38 \)
\( -38 + (-63) = -101 \)

Answer:

\(-101\)