Final answer:
The domain of function f(x) = -4x + 2 with the given range (10, 14, 18) would be the x-values that yield these range values when plugged into the function. However, the calculated x-values (-2, -3, -4) do not lie within the given interval 0 ≤ x ≤ 20, indicating a possible error in the provided information.
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined. Given that we have a function f(x) = -4x + 2, and we are provided with a range of values (10, 14, 18), we need to determine the corresponding x-values that produce this range. As the function represents a line, we can find the domain by solving for x in the equation f(x) = y for each y-value in the range.
- For y = 10: -4x + 2 = 10, solving for x gives x = -2.
- For y = 14: -4x + 2 = 14, solving for x gives x = -3.
- For y = 18: -4x + 2 = 18, solving for x gives x = -4.
Assuming the function f(x) is only defined for 0 ≤ x ≤ 20, only x-values within this interval are relevant for the domain. However, in this case, the x-values (-2, -3, and -4) are not within the allowed interval, suggesting there might be an error in the problem as stated or in the function provided. If these were the correct x-values, they would be excluded from the domain based on the given restrictions.