Question

F (x) = x cos²хопределите честность функций ​

Answer 1

Ответ:

нечетная

Объяснение:

f(-x) = f(x) - четная функция

f(-x) = -f(x) - нечетная функция

Подставим -x

f(-x) = -x*cos²-х = -x*cos²х = -f(x) - функция нечетная

Answer 2

To determine the parity of a function, we need to check whether the function satisfies one of two properties: even or odd.

1. Even Function: A function f(x) is even if it satisfies the property: f(-x) = f(x) for all x in its domain. Geometrically, this means the function is symmetric with respect to the y-axis.

2. Odd Function: A function f(x) is odd if it satisfies the property: f(-x) = -f(x) for all x in its domain. Geometrically, this means the function is symmetric with respect to the origin.

Now, let's examine the given function f(x) = x * cos²(x):

Step 1: Check for evenness: f(-x) = (-x) * cos²(-x) = (-x) * cos²(x)

f(x) = x * cos²(x)

The given function is not an even function because f(-x) is not equal to f(x).

Step 2: Check for oddness: f(-x) = (-x) * cos²(-x) = (-x) * cos²(x)

f(x) = x * cos²(x)

To check for oddness, we need to determine if f(-x) = -f(x). However, from the above expressions, we see that f(-x) = f(x) and not -f(x).

Therefore, the given function f(x) = x * cos²(x) is neither an even nor an odd function. It doesn't exhibit symmetry about the y-axis or the origin.