Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\frac{\left(e^{2}\right)^{x - 1}}{2} \left(x - 1\right) = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 1$$
Numerical solution$$x_{1} = -62.4578471989128$$
$$x_{2} = -106.417963206245$$
$$x_{3} = -14.9806772001439$$
$$x_{4} = -48.487646689892$$
$$x_{5} = -34.5463680381357$$
$$x_{6} = -32.5597813171015$$
$$x_{7} = -74.4419310233885$$
$$x_{8} = -24.6424295706756$$
$$x_{9} = -72.4441880676345$$
$$x_{10} = -42.5073396063464$$
$$x_{11} = -92.4262826664454$$
$$x_{12} = -94.4249341851903$$
$$x_{13} = -50.482252767615$$
$$x_{14} = -22.6757451532018$$
$$x_{15} = -82.4340741575283$$
$$x_{16} = -80.4358814217583$$
$$x_{17} = -36.5347052738485$$
$$x_{18} = 1$$
$$x_{19} = -98.4224109614399$$
$$x_{20} = -64.454745139734$$
$$x_{21} = -84.432358283505$$
$$x_{22} = -18.7755860151928$$
$$x_{23} = -58.464753641239$$
$$x_{24} = -40.5154118585931$$
$$x_{25} = -54.4727881654018$$
$$x_{26} = -44.5000993631074$$
$$x_{27} = -38.5244692579679$$
$$x_{28} = -60.4611748339881$$
$$x_{29} = -76.439801011308$$
$$x_{30} = -88.429174285909$$
$$x_{31} = -28.5937393694414$$
$$x_{32} = -16.8562161179393$$
$$x_{33} = -96.4236448887784$$
$$x_{34} = -102.420095524533$$
$$x_{35} = -104.419007861607$$
$$x_{36} = -90.4276945075164$$
$$x_{37} = -110.41599309682$$
$$x_{38} = -52.4773187883893$$
$$x_{39} = -56.4686132524805$$
$$x_{40} = -70.4465838765021$$
$$x_{41} = -78.437787586974$$
$$x_{42} = -86.4307270314252$$
$$x_{43} = -20.7185017258284$$
$$x_{44} = -30.5753760558308$$
$$x_{45} = -66.4518464300967$$
$$x_{46} = -68.4491316757143$$
$$x_{47} = -100.421228908762$$
$$x_{48} = -46.4935682921138$$
$$x_{49} = -26.6156935676912$$
$$x_{50} = -108.416959055435$$