Final answer:
To determine the domain of the function f(x) = √−9x+√1, solve for when the expression under the square root is non-negative. This gives the domain as [−∞, 1/9].
Step-by-step explanation:
The student is asking to find the domain of the function f(x) = √−9x+√1. To find the domain, we need to identify the set of all possible x-values that we can plug into the function without causing any mathematical errors such as taking the square root of a negative number or dividing by zero.
For the function given, since we have a square root operation, the expression inside the square root must be greater than or equal to zero. Therefore, we have the inequality: −9x + 1 ≥ 0.
By solving this inequality, we get x ≤ 1/9. Therefore, the domain of f(x) is [−∞, 1/9] in interval notation.