Question

найти область определения функции:у=4х/ корень квадратный 12-3х; помогите пожалуйста!

Answer 1

12-3х>0     -3х>-12      x<4 (-бесконечности; 4)

Answer 2

ОДЗ:

12-3x>0

-3x>-12

x<4

x принадлежит (-бесконеч; 4)

Answer 3

Finding the Domain of the Function

To find the domain of the function y = 4x / (sqrt(12 - 3x)), we need to consider the restrictions on the input values of x that would make the function undefined.

The function y = 4x / (sqrt(12 - 3x)) involves a square root, and the domain of a square root function is restricted by the requirement that the expression inside the square root must be non-negative.

The expression inside the square root, 12 - 3x, must be greater than or equal to 0 for the function to be defined.

Calculating the Domain

To find the domain, we solve the inequality 12 - 3x ≥ 0 for x.

12 - 3x ≥ 0 -3x ≥ -12 x ≤ 4

So, the domain of the function is x ≤ 4.

Therefore, the domain of the function y = 4x / (sqrt(12 - 3x)) is x ≤ 4.

This means that the function is defined for all real numbers x such that x ≤ 4.