Question

Найдите область определения функции у=корень квадратный из 4х-9х^2 ДАЮ 50 БАЛЛОВ!

Answer 1

Поищи в сайте у тебя есть номер пример N932

Answer 2

К.кв.(4х-9х^2)>=0
4х-9х^2>=0
4х-9х^2=0
х (4-9х)=0
х=0 или х=4/9
Рисуем прямую и отмечаем корни,раставляем знаки:
(-) (+) (-)
---.-----.------>
0 4/9
Ответ [0;4/9]

Answer 3

Finding the Domain of the Function

To find the domain of the function y = √(4x - 9x^2), we need to consider the values of x for which the function is defined and real. The domain of a square root function is the set of all real numbers greater than or equal to zero for which the expression inside the square root is non-negative.

The expression inside the square root, 4x - 9x^2, must be greater than or equal to zero for the function to be defined.

Calculating the Domain

The expression inside the square root, 4x - 9x^2, must be greater than or equal to zero: - 4x - 9x^2 ≥ 0

To find the values of x that satisfy this inequality, we can solve for the roots of the quadratic equation 4x - 9x^2 = 0 and then test the intervals between these roots.

Solving the Inequality

The roots of the quadratic equation 4x - 9x^2 = 0 can be found using the quadratic formula: - x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = -9, b = 4, and c = 0.

The roots of the equation are the values of x for which the expression 4x - 9x^2 equals zero.

Conclusion

The domain of the function y = √(4x - 9x^2) is the set of all real numbers x such that 4x - 9x^2 ≥ 0. This means the domain consists of the values of x for which the expression inside the square root is non-negative.

Note: The specific values of x that satisfy the inequality can be calculated using the quadratic formula and then testing the intervals between these roots.