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