Question

Y=3x^2+x функция четная или нет

Answer 1

Подставим в функцию (-х) и посмотрим, поменяет ли она знак на противоположный или нет.
f(-x)=
$3({ - x})^{2} + ( - x) = 3 {x}^{2} - x$
то есть функция поменяла знак частично. Значит, она ни четная, ни нечетная

Answer 2

To determine whether the function Y = 3x^2 + x is even or not, we need to check if it satisfies the property of even functions.

A function is considered even if it satisfies the following property: f(-x) = f(x) for all values of x in the domain of the function.

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

Y = 3x^2 + x

Now, let's find f(-x):

f(-x) = 3(-x)^2 + (-x) = 3x^2 - x

Now, we need to compare f(-x) with f(x):

f(-x) = 3x^2 - x f(x) = 3x^2 + x

The function Y = 3x^2 + x is even if f(-x) is equal to f(x) for all x.

As we can see, f(-x) = 3x^2 - x, and f(x) = 3x^2 + x.

Since f(-x) is NOT equal to f(x) (3x^2 - x ≠ 3x^2 + x), the given function Y = 3x^2 + x is NOT even.

In other words, the function Y = 3x^2 + x is NOT an even function.