Sure! Let's find the value of [tex]\( g(-n) \)[/tex] given the function [tex]\( g(n) = 3n + 1 \)[/tex].
Here's a detailed, step-by-step solution:
1. Identify the given function:
[tex]\[
g(n) = 3n + 1
\][/tex]
2. Substitute [tex]\(-n\)[/tex] into the function:
We need to find [tex]\( g(-n) \)[/tex]. This means we replace every occurrence of [tex]\( n \)[/tex] in [tex]\( g(n) \)[/tex] with [tex]\(-n\)[/tex].
3. Substitute [tex]\(-n\)[/tex] into the expression [tex]\( 3n + 1 \)[/tex]:
[tex]\[
g(-n) = 3(-n) + 1
\][/tex]
4. Simplify the expression:
[tex]\[
g(-n) = -3n + 1
\][/tex]
So, the value of [tex]\( g(-n) \)[/tex] is:
[tex]\[
g(-n) = -3n + 1
\][/tex]
This is the required solution.
