Question

Найти область определения функций у=√2-3х

Answer 1

Если корень из всего выражения, то
$y=\sqrt{2-3x}\\ D(y): \\ 2-3x\geq0\\ 3x-2\leq0\\ x\leq\frac{2}{3}\\ D(y)=\bigg(-\infty; \frac{2}{3} \bigg]$

Answer 2

To find the domain of the function $y = \sqrt{2 - 3x}$, we need to consider the values of $x$ for which the expression under the square root is non-negative. Remember that the square root of a negative number is not defined in the real number system.

The expression under the square root, $2 - 3x$, must be greater than or equal to zero:

$2 - 3x \geq 0$

Now, let's solve this inequality for $x$:

$2 \geq 3x$

$\frac{2}{3} \geq x$

So, the domain of the function is all real numbers $x$ such that $x \leq \frac{2}{3}$. In interval notation, the domain is $(-\infty, \frac{2}{3}]$.