Question

Y = 3cos(x)^2 - 1найдите область определения

Answer 1

Ответ:

Область определения вся числовая ось D(f)=(-∞;+∞) или x∈R

Пошаговое объяснение:

Answer 2

To find the domain of the function Y = 3cos(x)^2 - 1, we need to determine the values of x for which the function is defined.

The cosine function, cos(x), is defined for all real numbers. However, the expression 3cos(x)^2 involves squaring the cosine function, which means the result will always be non-negative since the square of any real number is non-negative.

So, for the function Y = 3cos(x)^2 - 1 to be defined, the expression 3cos(x)^2 must be non-negative. Thus, we have the following inequality:

3cos(x)^2 ≥ 0

To satisfy this inequality, cos(x)^2 must be greater than or equal to 0, which means cos(x) must be greater than or equal to 0 or cos(x) must be less than or equal to 0.

1. cos(x) ≥ 0 This condition is true for x in the interval [0, π/2] and [3π/2, 2π] (and in subsequent periods as well).

2. cos(x) ≤ 0 This condition is true for x in the interval [π/2, 3π/2] (and in subsequent periods as well).

Now, to find the overall domain, we take the intersection of these two intervals:

Domain of Y = 3cos(x)^2 - 1: [0, π/2] ∪ [3π/2, 2π]

So, the function Y = 3cos(x)^2 - 1 is defined for all x in the range [0, π/2] and [3π/2, 2π], and this pattern repeats in subsequent periods for x.