El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\operatorname{atan}{\left(\frac{13}{\left(x - 12\right)^{3}} \right)} + \frac{\sin{\left(x - 9 \right)}}{x^{2} - 81} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución numérica$$x_{1} = 52.4298004490239$$
$$x_{2} = -63.3763831396492$$
$$x_{3} = 75.2642011280125$$
$$x_{4} = 44.3665643221052$$
$$x_{5} = -31.9851186004864$$
$$x_{6} = 94.0308211696106$$
$$x_{7} = -72.5697275281099$$
$$x_{8} = 140.82650751175$$
$$x_{9} = -22.281461994801$$
$$x_{10} = 84.1535074077066$$
$$x_{11} = 38.6104862633758$$
$$x_{12} = -16.0286937840434$$
$$x_{13} = -91.433549206396$$
$$x_{14} = -25.6985781894203$$
$$x_{15} = -41.1254062863102$$
$$x_{16} = -38.2659572454688$$
$$x_{17} = -75.9319114138818$$
$$x_{18} = 77.8392602643122$$
$$x_{19} = -28.5554866371386$$
$$x_{20} = 81.5134656514425$$
$$x_{21} = -19.3986722071289$$
$$x_{22} = -69.6539818981402$$
$$x_{23} = 71.5162457041269$$
$$x_{24} = 65.1801664707372$$
$$x_{25} = -82.2101904240501$$
$$x_{26} = 69.024799329591$$
$$x_{27} = -101.047019007824$$
$$x_{28} = 90.4615805511166$$
$$x_{29} = 50.4396408162215$$
$$x_{30} = 87.7696350867141$$
$$x_{31} = 58.8232854202906$$
$$x_{32} = -78.8580147792537$$
$$x_{33} = 62.8001724084915$$
$$x_{34} = -88.4888136066665$$
$$x_{35} = -6.63355689266764$$
$$x_{36} = -34.8384983829641$$
$$x_{37} = 56.5991542447069$$
$$x_{38} = -66.2810949670056$$
$$x_{39} = 266.554634188786$$
$$x_{40} = 0.289382679980216$$
$$x_{41} = -97.7208287787063$$
$$x_{42} = -57.0990491159741$$
$$x_{43} = 1.58816662935336$$
$$x_{44} = -59.9921574732332$$
$$x_{45} = -94.7677638814346$$
$$x_{46} = -53.7030237675369$$
$$x_{47} = -85.1459513075987$$
$$x_{48} = 96.7651418478124$$
$$x_{49} = 45.9591332368927$$
$$x_{50} = 100.295762440176$$
$$x_{51} = -107.326555126364$$
$$x_{52} = 175.59584679483$$
$$x_{53} = 39.1908281002193$$
$$x_{54} = 304.261524599798$$
$$x_{55} = -9.83002379517778$$
$$x_{56} = -50.8218216402348$$
$$x_{57} = -3.78834083550013$$
$$x_{58} = -44.5443607076976$$
$$x_{59} = -13.0652663136774$$
$$x_{60} = -47.4139365248118$$