Question

Y=sqrt((9-x^2)|x-6|) Найти область определения функции

Answer 1

Смотри............................

Answer 2

To find the domain of the function, we need to determine the values of x for which the function Y is defined. The domain of the function consists of all the possible x-values that make the expression inside the square root non-negative, as well as ensuring that the expression inside the absolute value is valid.

1. Inside the square root, we have (9 - x^2). For the expression inside the square root to be non-negative, we must have:

   9 - x^2 ≥ 0

2. Inside the absolute value, we have (x - 6). For the expression inside the absolute value to be valid, we don't have any specific constraints.

Now, let's solve the inequalities step-by-step:

1. Solving 9 - x^2 ≥ 0: Add x^2 to both sides: 9 ≥ x^2 Take the square root of both sides, noting that we have to consider both positive and negative roots: ±√9 ≥ x ±3 ≥ x

2. The expression inside the absolute value is always valid since it doesn't involve any inequalities.

Now, we have two conditions to consider for the domain:

1. x must satisfy ±3 ≥ x
2. There are no additional constraints from the absolute value expression.

The domain of the function is the set of all x-values that satisfy both conditions. Therefore, the domain is given by:

Domain = {-3, -2, -1, 0, 1, 2, 3}