Certainly! Let's solve the given problem step-by-step.
We are given the function [tex]\( g(x) = -x^2 - x + 5 \)[/tex] and asked to evaluate it at [tex]\( x = -4 \)[/tex].
Here’s how you can find [tex]\( g(-4) \)[/tex]:
1. Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( g(x) \)[/tex]. That is, replace every [tex]\( x \)[/tex] in the expression with [tex]\(-4\)[/tex].
[tex]\[
g(-4) = -(-4)^2 - (-4) + 5
\][/tex]
2. Evaluate each term in the expression.
- Begin by calculating [tex]\((-4)^2\)[/tex]:
[tex]\[
(-4)^2 = 16
\][/tex]
- Then, apply the negative sign to this result:
[tex]\[
-(-4)^2 = -16
\][/tex]
3. Now, evaluate the second term [tex]\(-(-4)\)[/tex]:
[tex]\[
-(-4) = 4
\][/tex]
4. The third term remains as 5.
5. Combine all these results to get:
[tex]\[
g(-4) = -16 + 4 + 5
\][/tex]
6. Perform the addition and subtraction in sequence:
- First, add -16 and 4:
[tex]\[
-16 + 4 = -12
\][/tex]
- Then, add the remaining 5 to -12:
[tex]\[
-12 + 5 = -7
\][/tex]
Thus, the value of [tex]\( g(-4) \)[/tex] is:
[tex]\[
\boxed{-7}
\][/tex]
So, [tex]\( g(-4) = -7 \)[/tex]. The correct answer is option (2) [tex]\( -7 \)[/tex].
