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$$2 \left(\left(2 x + 1\right)^{2} \delta\left(x^{2} + x - 2\right) + \operatorname{sign}{\left(x^{2} + x - 2 \right)}\right) = 0$$
Solve this equationSolutions are not found,
maybe, the function has no inflections