Final answer:
The domain of the function f(x) = √(1/3x + 2) is x ≥ -6.
Step-by-step explanation:
The domain of the function f(x) = √(1/3x + 2) is the set of all real numbers that make the expression inside the square root valid.
To find this domain, we need to ensure that the expression 1/3x + 2 is not negative because the square root of a negative number is not real. We can solve this inequality:
1/3x + 2 ≥ 0
Subtracting 2 from both sides:
1/3x ≥ -2
Multiplying both sides by 3:
x ≥ -6
So, the domain of the function is x ≥ -6.