https://file.aiquickdraw.com/mathbot/file/1728892981265014v6duo.jpg

The problem asks for which values of \( x \) the expression \( \sqrt{5x + 20} \) is defined.

For a square root expression to be defined, the expression inside the square root must be non-negative. In other words:

\[
5x + 20 \geq 0
\]

Now, let's solve this inequality step by step:

\[
5x \geq -20
\]

\[
x \geq -4
\]

So, the expression \( \sqrt{5x + 20} \) is defined for \( x \geq -4 \).

Thus, the correct interval for \( x \) is:

\[
[-4, +\infty)
\]

In the image, this corresponds to the option \( [-4; +\infty) \).

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the domain change if the expression inside the square root had different coefficients?
2. What happens if you apply this logic to cube roots instead of square roots?
3. How can you graph the function \( y = \sqrt{5x + 20} \)?
4. What if the expression was \( \sqrt{5x - 20} \)? How would the solution change?
5. How do you determine the domain of more complex functions involving square roots and other operations?

**Tip:** Always check the expression inside the square root to ensure it is non-negative for the domain determination.

При яких значеннях x має зміст вираз √5x + 20?

Learn how to find the domain for the expression √(5x + 20). This problem focuses on algebraic concepts like inequalities and square roots, suitable for students in Grades 9-11.

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