To find the inverse of the function \( g(x) = (3x + 5)^2 \), you start by replacing \( g(x) \) with \( y \):
\[ y = (3x + 5)^2 \]
Next, switch \( x \) and \( y \):
\[ x = (3y + 5)^2 \]
Now, to solve for \( y \), you first take the square root of both sides:
\[ \sqrt{x} = 3y + 5 \quad \text{or} \quad -\sqrt{x} = 3y + 5 \]
Assuming we take the positive square root (the most common for inverse functions):
\[ 3y = \sqrt{x} - 5 \]
Now, solving for \( y \):
\[ y = \frac{\sqrt{x} - 5}{3} \]
This shows the process of switching the variables and solving for \( y \).
From the provided options, it appears there isn't a direct match for the final equation derived. However, based on the general form of some choices, the answer seems to relate most closely to rearranging terms and achieving a proportional representation.
None of the options provided directly reflect this simplified form. Nevertheless, the important aspect to highlight in the inverse finding process is properly switching the variables and isolating \( y \) after switching.
Given the listed responses, the closest might be:
y = (3x - 5)/2
But again, it's essential to clarify that it's not a direct representation of the inverse function obtained.