Question

Y= x-1/ x^-4x область определения

Answer 1

Знаменатель не может быть равен нулю
x^2-4 ≠ 0
(x+2)(x-2) ≠ 0
x ≠ -2, x ≠ 2

Answer 2

Equation and Domain

The equation is y = (x - 1) / (x^2 - 4x). To find the domain of this equation, we need to determine the values of x for which the equation is defined.

To find the domain, we need to consider the denominator of the equation, which is x^2 - 4x. We know that the denominator cannot be equal to zero because division by zero is undefined. So, we need to find the values of x that make the denominator equal to zero.

To solve the equation x^2 - 4x = 0, we can factor out an x: x(x - 4) = 0. This equation is satisfied when either x = 0 or x - 4 = 0. Therefore, the values of x that make the denominator zero are x = 0 and x = 4.

However, we need to exclude these values from the domain because they would result in division by zero. Therefore, the domain of the equation is all real numbers except x = 0 and x = 4.

The domain can be expressed as (-∞, 0) U (0, 4) U (4, ∞).