Answer:
A
Explanation:
Given quadratic function:

The domain of the given function is restricted to values of x less than or equal to zero. Therefore:
As 3x² ≥ 0, then range of the given function is restricted to values of y greater than or equal to -9.

To find the inverse of the given function, first interchange the x and y variables:

Now, solve the equation for y:

The range of the inverse function is the domain of the original function.
As the domain of the original function is restricted to x ≤ 0, then the range of the inverse function is restricted to y ≤ 0.
Therefore, the inverse function is the negative square root:

The domain of the inverse function is the range of the original function.
As the range of the original function is restricted to y ≥ -9, then the domain of the inverse function is restricted to x ≥ -9.

So the correct statement is:
- A) The inverse of y is equal to negative square root of the quantity x plus 9 over 3 end quantity such that x is greater than or equal to negative 9.