Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative$$\frac{2 \left(- \frac{6 x}{3 x + 1} + 1 + \frac{9 \left(x^{2} - 1\right)}{\left(3 x + 1\right)^{2}}\right)}{3 x + 1} = 0$$
Solve this equationSolutions are not found,
maybe, the function has no inflections