To determine the domain of the function [tex]\( f(x) = \frac{x}{4} \)[/tex] given that its range is [tex]\(\{28, 30, 32, 34, 36\}\)[/tex], we need to find the values of [tex]\( x \)[/tex] such that [tex]\( f(x) \)[/tex] equals each of these range values.
Given the range values [tex]\( \{28, 30, 32, 34, 36\} \)[/tex], you can set up equations for each value as follows:
1. [tex]\( f(x) = 28 \)[/tex] implies that:
[tex]\[
\frac{x}{4} = 28
\][/tex]
Multiplying both sides by 4, we get:
[tex]\[
x = 28 \times 4 = 112
\][/tex]
2. [tex]\( f(x) = 30 \)[/tex] implies that:
[tex]\[
\frac{x}{4} = 30
\][/tex]
Multiplying both sides by 4, we get:
[tex]\[
x = 30 \times 4 = 120
\][/tex]
3. [tex]\( f(x) = 32 \)[/tex] implies that:
[tex]\[
\frac{x}{4} = 32
\][/tex]
Multiplying both sides by 4, we get:
[tex]\[
x = 32 \times 4 = 128
\][/tex]
4. [tex]\( f(x) = 34 \)[/tex] implies that:
[tex]\[
\frac{x}{4} = 34
\][/tex]
Multiplying both sides by 4, we get:
[tex]\[
x = 34 \times 4 = 136
\][/tex]
5. [tex]\( f(x) = 36 \)[/tex] implies that:
[tex]\[
\frac{x}{4} = 36
\][/tex]
Multiplying both sides by 4, we get:
[tex]\[
x = 36 \times 4 = 144
\][/tex]
Therefore, the domain corresponding to the given range [tex]\(\{28, 30, 32, 34, 36\}\)[/tex] is [tex]\(\{112, 120, 128, 136, 144\}\)[/tex].
Thus, the correct answer is:
A. [tex]\(\{112, 120, 128, 136, 144\}\)[/tex]
