Final answer:
The domain of the function f(x) = (2/5) * sqrt(x) is all real numbers x ≥ 0, or in interval notation, [0, ∞). This is because square roots are only defined for non-negative real numbers.
Step-by-step explanation:
The domain of a function refers to all possible values that can be input into the function, usually represented by 'x'. For the given function f(x) = \frac{2}{5} \sqrt{x}, we need to determine the set of x-values for which the function is defined. Since we cannot take the square root of a negative number in the set of real numbers, the smallest value for 'x' must be 0. Thus, the domain of the function f(x) = \frac{2}{5} \sqrt{x} includes all real numbers greater than or equal to 0.
This is written mathematically as “x ≥ 0” or in interval notation as [0, ∞). It's important to note that, for real numbers, square roots are only defined for non-negative values, which is why the domain starts at 0 and continues to positive infinity.