Domains Were Never This Tough!!!

$f\left( x \right) \quad \ge \quad 0\quad ,\quad (For\quad All\quad Values\quad Of\quad x)\\ { x }^{ 2 }f(x)\quad +\quad f(1-x)\quad \ge \quad 0\quad ,\quad (For\quad All\quad Values\quad Of\quad x)\\ \therefore \quad 2x-{ x }^{ 4 }\quad \ge \quad 0\\ \quad Solving\quad The\quad Inequality\quad We\quad Get,\\ \quad \quad x\quad \in \quad [\quad 0\quad ,\quad { 2 }^{ 1/3 }]\\ So,\quad x\quad must\quad be\quad in\quad the\quad above\quad range\quad \\ and\quad 1-x\quad must\quad also\quad be\quad in\quad the\quad above\quad range\\ on\quad solving\quad that\quad we\quad get\\ x\quad \in \quad [0,1]\\ So\quad The\quad Answer\quad Is\quad \boxed { 100 }$