The problem asks us to find the domain of the function $d(x) = 4 - \frac{1}{5}x$ for the range $\{0, \frac{11}{5}, 4.5\}$. This means we need to find the corresponding $x$ values for each of the given $d(x)$ values.

1. Problem Description

The problem asks us to find the domain of the function $d(x) = 4 - \frac{1}{5}x$ for the range $\{0, \frac{11}{5}, 4.5\}$. This means we need to find the corresponding $x$ values for each of the given $d(x)$ values.

2. Solution Steps

We have the function $d(x) = 4 - \frac{1}{5}x$. We are given the range values $d(x) = 0$, $d(x) = \frac{11}{5}$, and $d(x) = 4.5$. We need to find the corresponding $x$ values for each of these.

First, let $d(x) = 0$:

$0 = 4 - \frac{1}{5}x$

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

$x = 4 \times 5 = 20$

Next, let $d(x) = \frac{11}{5}$:

$\frac{11}{5} = 4 - \frac{1}{5}x$

$\frac{11}{5} = \frac{20}{5} - \frac{1}{5}x$

$\frac{1}{5}x = \frac{20}{5} - \frac{11}{5} = \frac{9}{5}$

$x = \frac{9}{5} \times 5 = 9$

Finally, let $d(x) = 4.5 = \frac{9}{2}$:

$\frac{9}{2} = 4 - \frac{1}{5}x$

$\frac{9}{2} = \frac{8}{2} - \frac{1}{5}x$

$\frac{1}{5}x = \frac{8}{2} - \frac{9}{2} = -\frac{1}{2}$

$x = -\frac{1}{2} \times 5 = -\frac{5}{2} = -2.5$

So, the domain values are $20, 9, -2.5$.

3. Final Answer

$\{20, 9, -2.5\}$