To determine whether the function \(f(x) = \frac{1}{3x+2} + x^2\) is increasing or decreasing, we need to find its derivative \(f'(x)\).

The derivative of \(f(x)\) is given by:

\(f'(x) = \left[ -\left(3x+2\right)^{-2} \right] \times [3] + [2x]\)

Simplifying, we have:

\(f'(x) = -\frac{3}{(3x+2)^2} + 2x\)

For \(x < -1\), the term \(-\frac{3}{(3x+2)^2}\) is negative and dominates over \(2x\), making \(f'(x) < 0\).

Since \(f'(x) < 0\) for \(x < -1\), the function \(f\) is decreasing.