Sure, let's go through each of these items step-by-step based on the given tables for the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex].
1. Find [tex]\( f(5) \)[/tex]:
- Look at the value corresponding to [tex]\( n = 5 \)[/tex] in the table for [tex]\( f(n) \)[/tex].
- [tex]\( f(5) = 12 \)[/tex].
2. Find [tex]\( f(9) \)[/tex]:
- Look at the value corresponding to [tex]\( n = 9 \)[/tex] in the table for [tex]\( f(n) \)[/tex].
- [tex]\( f(9) = 32 \)[/tex].
3. Find [tex]\( n \)[/tex] that goes with [tex]\( f(n) = 22 \)[/tex]:
- Find the index [tex]\( n \)[/tex] where [tex]\( f(n) = 22 \)[/tex].
- The corresponding [tex]\( n \)[/tex] is 7.
4. Find [tex]\( n \)[/tex] that goes with [tex]\( f(n) = -3 \)[/tex]:
- Find the index [tex]\( n \)[/tex] where [tex]\( f(n) = -3 \)[/tex].
- The corresponding [tex]\( n \)[/tex] is 2.
5. Find [tex]\( g(3) \)[/tex]:
- Look at the value corresponding to [tex]\( n = 3 \)[/tex] in the table for [tex]\( g(n) \)[/tex].
- [tex]\( g(3) = 6 \)[/tex].
6. Find [tex]\( g(8) \)[/tex]:
- Look at the value corresponding to [tex]\( n = 8 \)[/tex] in the table for [tex]\( g(n) \)[/tex].
- [tex]\( g(8) = -29 \)[/tex].
7. Find [tex]\( n \)[/tex] that goes with [tex]\( g(n) = -1 \)[/tex]:
- Find the index [tex]\( n \)[/tex] where [tex]\( g(n) = -1 \)[/tex].
- The corresponding [tex]\( n \)[/tex] is 4.
8. Find [tex]\( n \)[/tex] that goes with [tex]\( g(n) = -43 \)[/tex]:
- Find the index [tex]\( n \)[/tex] where [tex]\( g(n) = -43 \)[/tex].
- The corresponding [tex]\( n \)[/tex] is 10.
So, the values are:
- [tex]\( f(5) = 12 \)[/tex]
- [tex]\( f(9) = 32 \)[/tex]
- [tex]\( n \)[/tex] for [tex]\( f(n) = 22 \)[/tex] is 7
- [tex]\( n \)[/tex] for [tex]\( f(n) = -3 \)[/tex] is 2
- [tex]\( g(3) = 6 \)[/tex]
- [tex]\( g(8) = -29 \)[/tex]
- [tex]\( n \)[/tex] for [tex]\( g(n) = -1 \)[/tex] is 4
- [tex]\( n \)[/tex] for [tex]\( g(n) = -43 \)[/tex] is 10
