Question

F(x)= x в 5степени +x. определить, является ли данная функция четной, нечетной или функцией общего вида

Answer 1

Функция является не четной

Answer 2

Function Analysis

To determine whether the given function F(x) = x^5 + x is even, odd, or of general form, we need to analyze its symmetry properties.

Even Function

A function is considered even if it satisfies the condition f(-x) = f(x) for all values of x in its domain. In other words, if replacing x with -x in the function yields the same result as the original function, then it is even.

Let's check if the given function satisfies this condition:

F(-x) = (-x)^5 + (-x) = -x^5 - x

Since F(-x) ≠ F(x), the given function is not even.

Odd Function

A function is considered odd if it satisfies the condition f(-x) = -f(x) for all values of x in its domain. In other words, if replacing x with -x in the function yields the negative of the original function, then it is odd.

Let's check if the given function satisfies this condition:

F(-x) = (-x)^5 + (-x) = -x^5 - x

Since F(-x) = -F(x), the given function is odd.

General Form

If a function is neither even nor odd, it is considered to be of general form.

Based on the analysis above, we can conclude that the given function F(x) = x^5 + x is an odd function.