Question

F(x)=✓6-3x^2 найти область определение функции

Answer 1

✓6-3х^2>=0

Оба выражения возводим в квадрат, чтобы избавиться от корня.

6-3х^2>=0

-3х^2>=-6

х^2>=2

х1>=✓2 х2>=-✓2

Ответ: [✓2;+бесконечность)

Answer 2

To find the domain of the function F(x) = √(6 - 3x^2), we need to identify the values of x for which the function is defined. The square root function (√) is defined only for non-negative values. This means that the expression inside the square root (√(6 - 3x^2)) must be greater than or equal to zero.

So, we set the expression inside the square root to be greater than or equal to zero and solve for x:

6 - 3x^2 ≥ 0

To solve this inequality, we can follow these steps:

Step 1: Subtract 6 from both sides of the inequality: -3x^2 ≥ -6

Step 2: Divide both sides by -3 (remember to reverse the inequality when dividing by a negative number): x^2 ≤ 2

Step 3: Take the square root of both sides. Since we are looking for the non-negative square root, we include a plus-minus symbol (±) on the right side: x ≤ ±√2

The domain of the function F(x) is the set of all x values that satisfy this inequality. In this case, the domain is (-√2, √2), which means all real numbers between -√2 and √2 (excluding -√2 and √2). The reason we exclude -√2 and √2 is that at these points, the expression inside the square root becomes zero, and the function is not defined for those values.