Question

Б)у=3/(2-х)^2 найти область определения фунции

Answer 1

Знаменатель не должен быть равен 0
(2-х)²≠0
2-х≠0
х≠2
D(y) = (-∞;2) (2;+∞)

Answer 2

To find the domain of the function $f(x) = \frac{3}{(2-x)^2}$, we need to identify all values of $x$ for which the function is defined.

The function $f(x)$ will be defined as long as the denominator $(2-x)^2$ is not equal to zero, as division by zero is undefined. So, we need to find the values of $x$ that make the denominator equal to zero and exclude them from the domain.

Setting the denominator equal to zero and solving for $x$:

$2 - x = 0$

$x = 2$

Now, since $x = 2$ makes the denominator zero, we have to exclude it from the domain. Thus, the domain of the function $f(x)$ is all real numbers except $x = 2$.

In interval notation, the domain can be expressed as:

$x \in (-\infty, 2) \cup (2, \infty)$