To perform the indicated operation, we need to follow the given steps:
1. Define the Functions:
- [tex]\( g(x) = x + 5 \)[/tex]
- [tex]\( f(x) = -x + 1 \)[/tex]
2. Compute [tex]\( g(-10) \)[/tex]:
- Substitute [tex]\( x = -10 \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(-10) = (-10) + 5 = -5
\][/tex]
3. Compute [tex]\( f(-10) \)[/tex]:
- Substitute [tex]\( x = -10 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-10) = -(-10) + 1 = 10 + 1 = 11
\][/tex]
4. Add the Results:
- Now, add the values obtained from [tex]\( g(-10) \)[/tex] and [tex]\( f(-10) \)[/tex]:
[tex]\[
g(-10) + f(-10) = -5 + 11 = 6
\][/tex]
So, the answer to the problem [tex]\( g(-10) + f(-10) \)[/tex] is [tex]\( 6 \)[/tex].
