The problem asks us to find the domain of the function $d(x) = 4 - \frac{1}{2}x$ for the range $\{0, \frac{5}{2}, 4.5\}$. In other words, we need to find the $x$ values that correspond to $d(x) = 0$, $d(x) = \frac{5}{2}$, and $d(x) = 4.5$.

1. Problem Description

The problem asks us to find the domain of the function $d(x) = 4 - \frac{1}{2}x$ for the range $\{0, \frac{5}{2}, 4.5\}$. In other words, we need to find the $x$ values that correspond to $d(x) = 0$, $d(x) = \frac{5}{2}$, and $d(x) = 4.5$.

2. Solution Steps

First, we find the $x$ value when $d(x) = 0$:

$0 = 4 - \frac{1}{2}x$

$\frac{1}{2}x = 4$

$x = 8$

Second, we find the $x$ value when $d(x) = \frac{5}{2}$:

$\frac{5}{2} = 4 - \frac{1}{2}x$

$\frac{1}{2}x = 4 - \frac{5}{2}$

$\frac{1}{2}x = \frac{8}{2} - \frac{5}{2}$

$\frac{1}{2}x = \frac{3}{2}$

$x = 3$

Third, we find the $x$ value when $d(x) = 4.5$:

$4.5 = 4 - \frac{1}{2}x$

$\frac{9}{2} = 4 - \frac{1}{2}x$

$\frac{1}{2}x = 4 - \frac{9}{2}$

$\frac{1}{2}x = \frac{8}{2} - \frac{9}{2}$

$\frac{1}{2}x = -\frac{1}{2}$

$x = -1$

Therefore, the domain for the given range is $8, 3, -1$.

3. Final Answer

$-1, 3, 8$