The given function is:

$F(x) = \sqrt{3x + 6}$

Domain of the function:

Since the square root function is only defined for non-negative values, we need to ensure that the expression inside the square root is greater than or equal to zero.

$3x + 6 \geq 0$

Solve for $x$:

$3x \geq -6$ $x \geq -2$

Thus, the domain of the function is:

$x \in [-2, \infty)$

Simplified Form:

This is already in its simplest form, as it's a square root function.

Would you like to know more details or have any questions about this?

Here are 5 related questions to explore:

1. What is the range of $F(x) = \sqrt{3x + 6}$?
2. How do you graph $F(x) = \sqrt{3x + 6}$?
3. How would the function change if we added a constant outside the square root, like $F(x) = \sqrt{3x + 6} + 2$?
4. Can you find the inverse of $F(x) = \sqrt{3x + 6}$?
5. How do you compute $F(2)$ for this function?

Tip: Always check the domain first for functions involving square roots to avoid undefined values.