Final answer:
The function f(x) = √(2 - 4x) is decreasing on the interval [0, 0.5] and not increasing on any interval within its domain because the expression inside the square root decreases as x increases.
Step-by-step explanation:
To determine the intervals where the function f(x) = √(2 - 4x) is increasing or decreasing, we need to consider its derivative. The first derivative of a function tells us about its slope. If the derivative is positive on an interval, the function is increasing; if it's negative, the function is decreasing. However, for a square root function like this one, the domain is also important to consider, as the function only exists where the expression inside the square root is non-negative.
The domain of f(x) = √(2 - 4x) is 0 ≤ x ≤ 0.5, since 2 - 4x must be greater than or equal to 0. Within this domain, the function is always decreasing because as x increases, the value of 2 - 4x decreases, leading to a smaller square root value for larger x.
Therefore, the function is decreasing on the interval [0, 0.5], and it is not increasing on any interval within its domain.