Question

Y=sqrt(x^2-64) НАЙТИ ОБЛАСТЬ ОПРЕДЕЛЕНИЯ ФУНКЦИИ (:

Answer 1

X²-64≥0
X²≥64
X≥8 или X≤-8

Answer 2

Finding the Domain of the Function

To find the domain of the function Y = sqrt(x^2 - 64), we need to determine the values of x for which the function is defined.

The function involves taking the square root of the expression (x^2 - 64). For the square root to be defined, the expression inside the square root must be greater than or equal to zero.

So, we need to solve the inequality x^2 - 64 >= 0 to find the values of x that satisfy this condition.

To solve the inequality, we can factor the expression x^2 - 64 as (x - 8)(x + 8) and set it equal to zero:

(x - 8)(x + 8) >= 0

Now, we can determine the sign of the expression (x - 8)(x + 8) for different intervals of x:

1. When x < -8, both factors (x - 8) and (x + 8) are negative, so their product is positive. 2. When -8 < x < 8, the factor (x - 8) is negative, and the factor (x + 8) is positive, so their product is negative. 3. When x > 8, both factors (x - 8) and (x + 8) are positive, so their product is positive.

From this analysis, we can see that the expression (x - 8)(x + 8) is non-negative (greater than or equal to zero) when x <= -8 or x >= 8.

Therefore, the domain of the function Y = sqrt(x^2 - 64) is x <= -8 or x >= 8.

Example Values

Here are some example values of x and their corresponding values of Y:

1. For x = -10, Y = sqrt((-10)^2 - 64) = sqrt(100 - 64) = sqrt(36) = 6. 2. For x = 0, Y = sqrt((0)^2 - 64) = sqrt(0 - 64) = sqrt(-64), which is not a real number. 3. For x = 10, Y = sqrt((10)^2 - 64) = sqrt(100 - 64) = sqrt(36) = 6.

Please note that these are just a few examples, and the function can take on other values for different values of x within the domain.

I hope this helps! Let me know if you have any further questions.