Question

Найти область определения функции: y=√(3x-4)* √(x-2)

Answer 1

3x-4>=o x-2>=0

3x>=4 x>=2

X>=4/3

X€[2,+бесконечность)

Answer 2

To find the domain of the function $y = \sqrt{(3x - 4)} \cdot \sqrt{(x - 2)}$, we need to consider the values of $x$ that make the expression inside the square roots non-negative.

1. For the expression $3x - 4$ to be non-negative, we require: $3x - 4 \geq 0$ $3x \geq 4$ $x \geq \frac{4}{3}$

2. For the expression $x - 2$ to be non-negative, we require: $x - 2 \geq 0$ $x \geq 2$

Now, to ensure both square roots are defined, both $3x - 4$ and $x - 2$ must be non-negative: $3x - 4 \geq 0 \quad \text{and} \quad x - 2 \geq 0$

This means we need to find the values of $x$ that satisfy both inequalities: $x \geq \frac{4}{3} \quad \text{and} \quad x \geq 2$

Since $x$ must satisfy both conditions, the domain of the function is the intersection of the two intervals: $x \geq 2$

Thus, the domain of the function is $x \geq 2$.