Final answer:
The function f(x) = 2(x^2) - 5 is decreasing over the interval (-∞, 0), however, the closest answer choice provided is (-∞, 3), as the function decreases to the left of the vertex at x = 0.
Step-by-step explanation:
To determine over which interval the function f(x) = 2(x^2) - 5 is decreasing, we first need to find the vertex of this parabola. Since this is a quadratic function in the form of f(x) = ax^2 + bx + c, the vertex can be found at x = -b/(2a). However, since there is no b term in our function, the vertex occurs at x = 0. The coefficient of x^2 is positive, meaning the parabola opens upwards, so the function is decreasing to the left of the vertex and increasing to the right of the vertex.
Therefore, the function f(x) is decreasing over the interval (-∞, 0). None of the answer choices provided directly match this interval, so there may be a typo in the question. Consequently, based on the intervals given, the closest option to the correct answer would be a) (-∞, 3), as it includes the range where the function is indeed decreasing, even though it's more extensive than necessary.