Question

Область определения функции y=x+1/x^2-4

Answer 1

Решение
y= (x + 1) / (x^2 - 4)
x² - 4 > 0
x²- 4 = 0
x² = 4
x₁ = - 2
x₂ = 2
D(y) = (- ∞ ; - 2)∪(2 ; + ∞)

Answer 2

To find the domain of the function $y = \frac{x + 1}{x^2 - 4}$, we need to consider the values of $x$ that make the expression well-defined. Specifically, we need to avoid any values of $x$ that would result in division by zero, as that would make the function undefined.

The expression $x^2 - 4$ cannot be zero, as division by zero is undefined. Therefore, we must exclude any values of $x$ that make the denominator equal to zero.

To find those values, we set $x^2 - 4 = 0$ and solve for $x$:

$x^2 - 4 = 0$ $x^2 = 4$ $x = \pm 2$

So, the function is undefined when $x = 2$ and $x = -2$.

Thus, the domain of the function is all real numbers except $x = 2$ and $x = -2$:

$\text{Domain} = (-\infty, -2) \cup (-2, 2) \cup (2, \infty)$