Question

let f and g be defined by the table to the right. find the following.
\\(\sqrt{f(-4) - f(-3)} - g(-1)^2 + f(-5) + g(-1) \cdot g(-4)\\)

x	f(x)	g(x)
-4	7	8
-3	-9	9
-2	-8	-7
-1	-7	-3

\\(\sqrt{f(-4) - f(-3)} - g(-1)^2 + f(-5) + g(-1) \cdot g(-4) = \square\\)
(simplify your answer.)

Explanation:

Step1: Find values from table

From the table:

• \( f(-4) = 7 \), \( f(-3) = -9 \), \( g(-1) = -3 \), \( f(-5) = 3 \), \( g(-4) = 8 \)

Step2: Substitute into the expression

First, calculate \( f(-4) - f(-3) \):
\( 7 - (-9) = 7 + 9 = 16 \)

Then, \( \sqrt{f(-4) - f(-3)} = \sqrt{16} = 4 \)

Next, \( [g(-1)]^2 = (-3)^2 = 9 \)

\( f(-5) = 3 \)

\( g(-1) \cdot g(-4) = (-3) \cdot 8 = -24 \)

Now substitute all into the original expression:
\( 4 - 9 + 3 + (-24) \)

Step3: Simplify the expression

Calculate step by step:
\( 4 - 9 = -5 \)
\( -5 + 3 = -2 \)
\( -2 + (-24) = -26 \)

Answer:

\(-26\)