Question

Найдите область допустимых значений функции

Answer 1

1) 4 - x² ≥ 0
x² ≤ 4
x ∈ [-2; 2]
2) x ≠ 0
Ответ: x ∈ [-2; 0) ∪ (0; 2]

Answer 2

Finding the Domain of a Function

To find the domain of a function, we need to consider the restrictions on the input values that the function can accept. Let's analyze the provided information to determine the domain of the function.

**Source* provides the function \(y=x^{4}-5x^{3}+6x^{2}\) and the interval \([1; 4]\) for \(x\).

The domain of a function is the set of all possible input values (independent variable) for which the function is defined. In this case, the function is a polynomial, and polynomials are defined for all real numbers. Therefore, the domain of the function \(y=x^{4}-5x^{3}+6x^{2}\) is all real numbers.

So, the domain of the function \(y=x^{4}-5x^{3}+6x^{2}\) is all real numbers.

This conclusion is based on the general understanding of polynomial functions, which are defined for all real numbers.

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