Question

У = √(3х-6) + √(2х-11)

Answer 1

Если не ошибаюсь,то так.......

Answer 2

To analyze the function $У = \sqrt{3x-6} + \sqrt{2x-11}$, we need to consider its domain, any restrictions on the variables, and how it behaves.

1. Domain: To find the domain of the function, we need to consider the values of $x$ that make both square root expressions real and non-negative. For real numbers, the square root of a non-negative number is defined. So, we set the radicands (the expressions inside the square roots) greater than or equal to zero:

$$\begin{align*} 3x - 6 &\geq 0 \\ 2x - 11 &\geq 0 \end{align*}$$

Solving each inequality:

$$\begin{align*} 3x - 6 &\geq 0 \quad \Rightarrow \quad 3x \geq 6 \quad \Rightarrow \quad x \geq 2 \\ 2x - 11 &\geq 0 \quad \Rightarrow \quad 2x \geq 11 \quad \Rightarrow \quad x \geq \frac{11}{2} \end{align*}$$

So, the domain of the function is $x \geq \frac{11}{2}$ or $x \geq 2$.

2. Behaviour: The function $У = \sqrt{3x-6} + \sqrt{2x-11}$ consists of two square root terms, each dependent on $x$. As $x$ increases, both terms will also increase. The overall value of the function will be the sum of the two square root expressions, and it will also increase with $x$.

3. Graph: To get a visual understanding of the function, we can plot it. However, due to the complexity of square root functions, it's challenging to provide a graph without specific values of $x$. Nonetheless, you can use graphing software or calculators to plot the function for specific ranges of $x$ within its domain.

Keep in mind that the function will have an undefined value if it encounters negative values inside the square roots, which is outside the domain.