Question

Y=✓4x-x^2 область визначення под корням всё вырожение

Answer 1

Вот ОДЗ))))))))))))...

Answer 2

To determine the domain of the expression under the square root (√), we need to find the values of 'x' for which the expression inside the square root is non-negative (i.e., greater than or equal to zero). This is because square roots of negative numbers are not defined in the real number system.

The expression under the square root is:

√(4x - x^2)

To find the domain, we set the expression inside the square root greater than or equal to zero and solve the inequality:

4x - x^2 ≥ 0

To solve this inequality, we first factor it:

x(4 - x) ≥ 0

Now, we find the critical points by setting the expression equal to zero:

x(4 - x) = 0

Setting each factor to zero:

x = 0 4 - x = 0 x = 4

Now, we test the intervals created by the critical points and check if the inequality holds true.

For x < 0: Choose x = -1 (a value less than 0) (-1)(4 - (-1)) = (-1)(5) = -5 < 0 (False)

For 0 < x < 4: Choose x = 1 (a value between 0 and 4) (1)(4 - 1) = 3 > 0 (True)

For x > 4: Choose x = 5 (a value greater than 4) (5)(4 - 5) = (5)(-1) = -5 < 0 (False)

The solution is true for the interval 0 < x < 4. So, the domain of the expression is:

0 < x < 4

In interval notation, the domain is written as (0, 4).