To find the total cups of coffee made by Anna and Zoe today, we first need to add their individual contributions. The functions representing the total cups of coffee made by Anna and Zoe are given by [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] respectively.
[tex]\[
f(x) = 5x - 2
\][/tex]
[tex]\[
g(x) = 4x + 1
\][/tex]
To get the combined total cups of coffee made, we define a new function, [tex]\( T(x) \)[/tex], which is the sum of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
T(x) = f(x) + g(x) = (5x - 2) + (4x + 1) = 9x - 1
\][/tex]
Now let’s evaluate this total function [tex]\( T(x) \)[/tex] at different values of [tex]\( x \)[/tex] according to the given options:
1. For [tex]\( x - 1 \)[/tex]:
[tex]\[
T(1) = 9(1) - 1 = 9 - 1 = 8
\][/tex]
2. For [tex]\( x - 3 \)[/tex]:
[tex]\[
T(3) = 9(3) - 1 = 27 - 1 = 26
\][/tex]
3. For [tex]\( 9x + 1 \)[/tex]:
This doesn't directly correspond to a specific [tex]\( x \)[/tex] value using the same [tex]\( T(x) \)[/tex] formulation. Thus the answer would be a misfit in context.
[tex]\[
\text{Evaluating the function for an \( x \) that makes sense, like T(0)}: T(0) = 9(0) - 1 = -1
\][/tex]
4. For [tex]\( 9x - 1 \)[/tex]:
Compute cumulative functions simplistically:
[tex]\[
T(1) + T(0) - 2 = 9(1)-1 + 9(0)-1 -2
= (8) + (-1) - 2 = 5
\][/tex]
The final evaluated results for the given options are:
```
x-1: 8
x-3: 26
9x+1: -1
9x-1: 5
```
These evaluations represent the total cups of coffee made by both Anna and Zoe today based on the different x values and interpretations given in the question.
