Final answer:
The domain of the function f(x) = \sqrt{-9x + 1} consists of all real numbers x such that x is less than or equal to 1/9.
Step-by-step explanation:
To find the domain of f(x) = \sqrt{-9x + 1}, we need to ensure that the expression under the square root is non-negative, since the square root of a negative number is not defined in the set of real numbers. This means we have to solve the inequality -9x + 1 ≥ 0.
Let's solve the inequality step-by-step:
- Start by adding 9x to both sides: 1 ≥ 9x.
- Then divide both sides by 9: \frac{1}{9} ≥ x.
This gives us our domain: x ≤ \frac{1}{9}. This means that the function f(x) is defined for all real values of x that are less than or equal to \frac{1}{9}.