I am not sure I am writing this correctly:

What is the domain of the function
y=3(sq rt)6x+42
• x ≥ 0
• x ≤ 7
• x ≥ –6
• x ≥ –7

From the choices of answers, I think you typed the equation incorrectly

Looks like it should be
y = 3√(6x+42)
since we cannot take the square root of negatives,
6x + 42 ≥ 0
6x ≥ -42
x ≥ -7 , which is your last choice.

To determine the domain of a function, we need to identify the set of possible values for the independent variable (in this case, x) that would produce a valid output (y).

In this function, y = 3√(6x + 42). The only limitation specified for x is x ≥ 0. Therefore, any value of x that satisfies this condition would be valid.

From the options provided:
1. x ≥ 0: This option satisfies the given condition and includes all values of x greater than or equal to 0. Hence, it is a valid domain for the function.

2. x ≤ 7: This condition restricts the values of x to be less than or equal to 7, but it does not consider the x ≥ 0 condition mentioned earlier. So, it is not a valid domain for this function.

3. x ≥ –6: This condition includes all values of x greater than or equal to -6. It satisfies the x ≥ 0 requirement and therefore, is a valid domain.

4. x ≥ –7: Similar to the previous option, this condition includes all values of x greater than or equal to -7. It satisfies the x ≥ 0 requirement, making it a valid domain.

Therefore, the valid domains for the given function are options 1, 3, and 4: x ≥ 0, x ≥ –6, and x ≥ –7.