Question

Область визначення функції y = 3/ √2-x

Answer 1

Відповідь:якщо під знаком кореня 2-х,то D(f) =x є (-нескінченність; 2). Якщо там тільки 2 під коренем, то D(f) = x є R\ {√2}.

Покрокове пояснення:

Answer 2

To determine the domain of the function $y = \frac{3}{\sqrt{2-x}}$, we need to consider the values of $x$ for which the function is defined. The domain is the set of all valid input values that will produce a real output for the given function.

In this case, there are two things to consider:

1. The denominator of the fraction cannot be equal to zero because division by zero is undefined.
2. The expression under the square root ($2-x$) must be non-negative since taking the square root of a negative number would result in complex numbers, not real numbers.

Let's find the restrictions:

1. $2-x \neq 0$ (to avoid division by zero) $x \neq 2$

2. $2-x \geq 0$ (to ensure the expression under the square root is non-negative) $-x \geq -2$ $x \leq 2$

Combining the two conditions, the domain of the function is: $x \in (-\infty, 2)$ (excluding 2)