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The given function is:

\[
g(x) = \sqrt{5x + 25}
\]

To determine the domain of the function \( g(x) \), we need to ensure that the expression under the square root is non-negative, because the square root of a negative number is not real (for real-valued functions).

So, we solve for:

\[
5x + 25 \geq 0
\]

Subtract 25 from both sides:

\[
5x \geq -25
\]

Now, divide by 5:

\[
x \geq -5
\]

Thus, the domain of \( g(x) \) is all values of \( x \) such that \( x \geq -5 \).

In interval notation, the domain is:

\[
[-5, \infty)
\]

Would you like more details or have any further questions?

Here are 5 related questions to explore:

1. How do you find the domain of a function with multiple terms inside the square root?
2. What happens if the inequality results in no real solutions?
3. How do you express the domain for a logarithmic function?
4. Can you explain how to graph the domain of this function on a number line?
5. How do transformations (shifting or stretching) affect the domain of square root functions?

**Tip:** Always remember, the domain of a square root function requires the expression inside the square root to be greater than or equal to zero.

Find the domain of the function: g(x) = √(5x + 25).

Learn how to find the domain of the function g(x) = √(5x + 25) by solving the inequality 5x + 25 ≥ 0. This problem involves understanding square root functions and algebraic inequalities. Suitable for students in Grades 8-10.

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