To find the domain corresponding to the given range values of the function [tex]\( f(x) = 7x - 2.7 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] (the domain) that produce the specified range values. The function [tex]\( f(x) = 7x - 2.7 \)[/tex] can be solved for [tex]\( x \)[/tex]:
1. Given [tex]\( y = 7x - 2.7 \)[/tex], we can solve for [tex]\( x \)[/tex] by isolating it on one side of the equation:
[tex]\[ y = 7x - 2.7 \][/tex]
2. Add [tex]\( 2.7 \)[/tex] to both sides:
[tex]\[ y + 2.7 = 7x \][/tex]
3. Divide both sides by [tex]\( 7 \)[/tex]:
[tex]\[ x = \frac{y + 2.7}{7} \][/tex]
We will use this equation to find the value of [tex]\( x \)[/tex] for each given [tex]\( y \)[/tex] in the range.
- For [tex]\( y = 14.1 \)[/tex]:
[tex]\[ x = \frac{14.1 + 2.7}{7} = \frac{16.8}{7} = 2.4 \][/tex]
- For [tex]\( y = 30.9 \)[/tex]:
[tex]\[ x = \frac{30.9 + 2.7}{7} = \frac{33.6}{7} = 4.8 \][/tex]
- For [tex]\( y = 41.4 \)[/tex]:
[tex]\[ x = \frac{41.4 + 2.7}{7} = \frac{44.1}{7} = 6.3 \][/tex]
- For [tex]\( y = 58.9 \)[/tex]:
[tex]\[ x = \frac{58.9 + 2.7}{7} = \frac{61.6}{7} = 8.8 \][/tex]
- For [tex]\( y = 68 \)[/tex]:
[tex]\[ x = \frac{68 + 2.7}{7} = \frac{70.7}{7} = 10.1 \][/tex]
Therefore, the domain corresponding to the given range values [tex]\( \{14.1, 30.9, 41.4, 58.9, 68\} \)[/tex] is [tex]\(\{2.4, 4.8, 6.3, 8.8, 10.1\}\)[/tex].
Thus, the domain is [tex]\( \boxed{2.4, 4.8, 6.3, 8.8, 10.1} \)[/tex].
