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Das ist zum Beispiel erfüllt, wenn ",[569,1133,1135,1148],{"className":1134},[572],[569,1136,1138],{"className":1137},[576],[578,1139,1140],{"xmlns":580},[582,1141,1142,1146],{},[585,1143,1144],{},[588,1145,590],{},[592,1147,590],{"encoding":594},[569,1149,1151],{"className":1150,"ariaHidden":599},[598],[569,1152,1154,1157],{"className":1153},[603],[569,1155],{"className":1156,"style":608},[607],[569,1158,590],{"className":1159,"style":614},[612,613]," streng monoton steigt oder fällt. Notfalls schränkt man den Definitionsbereich ein.",[565,1162,1163,1164,1232],{},"So bestimmt man ",[569,1165,1167,1188],{"className":1166},[572],[569,1168,1170],{"className":1169},[576],[578,1171,1172],{"xmlns":580},[582,1173,1174,1186],{},[585,1175,1176],{},[696,1177,1178,1180],{},[588,1179,590],{},[585,1181,1182,1184],{},[703,1183,705],{},[707,1185,709],{},[592,1187,712],{"encoding":594},[569,1189,1191],{"className":1190,"ariaHidden":599},[598],[569,1192,1194,1197],{"className":1193},[603],[569,1195],{"className":1196,"style":722},[607],[569,1198,1200,1203],{"className":1199},[612],[569,1201,590],{"className":1202,"style":614},[612,613],[569,1204,1206],{"className":1205},[732],[569,1207,1209],{"className":1208},[736],[569,1210,1212],{"className":1211},[740],[569,1213,1215],{"className":1214,"style":745},[744],[569,1216,1217,1220],{"style":748},[569,1218],{"className":1219,"style":753},[752],[569,1221,1223],{"className":1222},[757,758,759,760],[569,1224,1226,1229],{"className":1225},[612,760],[569,1227,705],{"className":1228},[612,760],[569,1230,709],{"className":1231},[612,760],":",[1234,1235,1236,1336],"ol",{},[1237,1238,1239,1306,1307,1335],"li",{},[569,1240,1242,1266],{"className":1241},[572],[569,1243,1245],{"className":1244},[576],[578,1246,1247],{"xmlns":580},[582,1248,1249,1263],{},[585,1250,1251,1253,1255,1257,1259,1261],{},[588,1252,661],{},[703,1254,874],{},[588,1256,590],{},[703,1258,859],{"stretchy":864},[588,1260,630],{},[703,1262,869],{"stretchy":864},[592,1264,1265],{"encoding":594},"y = f(x)",[569,1267,1269,1287],{"className":1268,"ariaHidden":599},[598],[569,1270,1272,1275,1278,1281,1284],{"className":1271},[603],[569,1273],{"className":1274,"style":673},[607],[569,1276,661],{"className":1277,"style":677},[612,613],[569,1279],{"className":1280,"style":991},[881],[569,1282,874],{"className":1283},[995],[569,1285],{"className":1286,"style":991},[881],[569,1288,1290,1294,1297,1300,1303],{"className":1289},[603],[569,1291],{"className":1292,"style":1293},[607],"height:1em;vertical-align:-0.25em;",[569,1295,590],{"className":1296,"style":614},[612,613],[569,1298,859],{"className":1299},[963],[569,1301,630],{"className":1302},[612,613],[569,1304,869],{"className":1305},[981]," nach ",[569,1308,1310,1323],{"className":1309},[572],[569,1311,1313],{"className":1312},[576],[578,1314,1315],{"xmlns":580},[582,1316,1317,1321],{},[585,1318,1319],{},[588,1320,630],{},[592,1322,630],{"encoding":594},[569,1324,1326],{"className":1325,"ariaHidden":599},[598],[569,1327,1329,1332],{"className":1328},[603],[569,1330],{"className":1331,"style":642},[607],[569,1333,630],{"className":1334},[612,613]," auflösen.",[1237,1337,1338,1366,1367,1395,1396,1424],{},[569,1339,1341,1354],{"className":1340},[572],[569,1342,1344],{"className":1343},[576],[578,1345,1346],{"xmlns":580},[582,1347,1348,1352],{},[585,1349,1350],{},[588,1351,630],{},[592,1353,630],{"encoding":594},[569,1355,1357],{"className":1356,"ariaHidden":599},[598],[569,1358,1360,1363],{"className":1359},[603],[569,1361],{"className":1362,"style":642},[607],[569,1364,630],{"className":1365},[612,613]," und ",[569,1368,1370,1383],{"className":1369},[572],[569,1371,1373],{"className":1372},[576],[578,1374,1375],{"xmlns":580},[582,1376,1377,1381],{},[585,1378,1379],{},[588,1380,661],{},[592,1382,661],{"encoding":594},[569,1384,1386],{"className":1385,"ariaHidden":599},[598],[569,1387,1389,1392],{"className":1388},[603],[569,1390],{"className":1391,"style":673},[607],[569,1393,661],{"className":1394,"style":677},[612,613]," vertauschen, damit die Variable wieder ",[569,1397,1399,1412],{"className":1398},[572],[569,1400,1402],{"className":1401},[576],[578,1403,1404],{"xmlns":580},[582,1405,1406,1410],{},[585,1407,1408],{},[588,1409,630],{},[592,1411,630],{"encoding":594},[569,1413,1415],{"className":1414,"ariaHidden":599},[598],[569,1416,1418,1421],{"className":1417},[603],[569,1419],{"className":1420,"style":642},[607],[569,1422,630],{"className":1423},[612,613]," heißt.",[565,1426,1427,1428,1496,1497,682,1500,1551],{},"Der Graph von ",[569,1429,1431,1452],{"className":1430},[572],[569,1432,1434],{"className":1433},[576],[578,1435,1436],{"xmlns":580},[582,1437,1438,1450],{},[585,1439,1440],{},[696,1441,1442,1444],{},[588,1443,590],{},[585,1445,1446,1448],{},[703,1447,705],{},[707,1449,709],{},[592,1451,712],{"encoding":594},[569,1453,1455],{"className":1454,"ariaHidden":599},[598],[569,1456,1458,1461],{"className":1457},[603],[569,1459],{"className":1460,"style":722},[607],[569,1462,1464,1467],{"className":1463},[612],[569,1465,590],{"className":1466,"style":614},[612,613],[569,1468,1470],{"className":1469},[732],[569,1471,1473],{"className":1472},[736],[569,1474,1476],{"className":1475},[740],[569,1477,1479],{"className":1478,"style":745},[744],[569,1480,1481,1484],{"style":748},[569,1482],{"className":1483,"style":753},[752],[569,1485,1487],{"className":1486},[757,758,759,760],[569,1488,1490,1493],{"className":1489},[612,760],[569,1491,705],{"className":1492},[612,760],[569,1494,709],{"className":1495},[612,760]," entsteht durch ",[680,1498,1499],{},"Spiegeln an der Winkelhalbierenden",[569,1501,1503,1521],{"className":1502},[572],[569,1504,1506],{"className":1505},[576],[578,1507,1508],{"xmlns":580},[582,1509,1510,1518],{},[585,1511,1512,1514,1516],{},[588,1513,661],{},[703,1515,874],{},[588,1517,630],{},[592,1519,1520],{"encoding":594},"y = x",[569,1522,1524,1542],{"className":1523,"ariaHidden":599},[598],[569,1525,1527,1530,1533,1536,1539],{"className":1526},[603],[569,1528],{"className":1529,"style":673},[607],[569,1531,661],{"className":1532,"style":677},[612,613],[569,1534],{"className":1535,"style":991},[881],[569,1537,874],{"className":1538},[995],[569,1540],{"className":1541,"style":991},[881],[569,1543,1545,1548],{"className":1544},[603],[569,1546],{"className":1547,"style":642},[607],[569,1549,630],{"className":1550},[612,613],". Definitions- und Wertebereich tauschen dabei die Rollen.",[560,1553,1555],{"id":1554},"beispiele","Beispiele",[565,1557,1558,1658,1659,1737,1738,1884],{},[569,1559,1561,1594],{"className":1560},[572],[569,1562,1564],{"className":1563},[576],[578,1565,1566],{"xmlns":580},[582,1567,1568,1591],{},[585,1569,1570,1572,1574,1576,1578,1580,1583,1585,1588],{},[588,1571,590],{},[703,1573,859],{"stretchy":864},[588,1575,630],{},[703,1577,869],{"stretchy":864},[703,1579,874],{},[707,1581,1582],{},"2",[588,1584,630],{},[703,1586,1587],{},"+",[707,1589,1590],{},"3",[592,1592,1593],{"encoding":594},"f(x) = 2x + 3",[569,1595,1597,1624,1648],{"className":1596,"ariaHidden":599},[598],[569,1598,1600,1603,1606,1609,1612,1615,1618,1621],{"className":1599},[603],[569,1601],{"className":1602,"style":1293},[607],[569,1604,590],{"className":1605,"style":614},[612,613],[569,1607,859],{"className":1608},[963],[569,1610,630],{"className":1611},[612,613],[569,1613,869],{"className":1614},[981],[569,1616],{"className":1617,"style":991},[881],[569,1619,874],{"className":1620},[995],[569,1622],{"className":1623,"style":991},[881],[569,1625,1627,1631,1634,1637,1641,1645],{"className":1626},[603],[569,1628],{"className":1629,"style":1630},[607],"height:0.7278em;vertical-align:-0.0833em;",[569,1632,1582],{"className":1633},[612],[569,1635,630],{"className":1636},[612,613],[569,1638],{"className":1639,"style":1640},[881],"margin-right:0.2222em;",[569,1642,1587],{"className":1643},[1644],"mbin",[569,1646],{"className":1647,"style":1640},[881],[569,1649,1651,1655],{"className":1650},[603],[569,1652],{"className":1653,"style":1654},[607],"height:0.6444em;",[569,1656,1590],{"className":1657},[612],". Aus ",[569,1660,1662,1686],{"className":1661},[572],[569,1663,1665],{"className":1664},[576],[578,1666,1667],{"xmlns":580},[582,1668,1669,1683],{},[585,1670,1671,1673,1675,1677,1679,1681],{},[588,1672,661],{},[703,1674,874],{},[707,1676,1582],{},[588,1678,630],{},[703,1680,1587],{},[707,1682,1590],{},[592,1684,1685],{"encoding":594},"y = 2x + 3",[569,1687,1689,1707,1728],{"className":1688,"ariaHidden":599},[598],[569,1690,1692,1695,1698,1701,1704],{"className":1691},[603],[569,1693],{"className":1694,"style":673},[607],[569,1696,661],{"className":1697,"style":677},[612,613],[569,1699],{"className":1700,"style":991},[881],[569,1702,874],{"className":1703},[995],[569,1705],{"className":1706,"style":991},[881],[569,1708,1710,1713,1716,1719,1722,1725],{"className":1709},[603],[569,1711],{"className":1712,"style":1630},[607],[569,1714,1582],{"className":1715},[612],[569,1717,630],{"className":1718},[612,613],[569,1720],{"className":1721,"style":1640},[881],[569,1723,1587],{"className":1724},[1644],[569,1726],{"className":1727,"style":1640},[881],[569,1729,1731,1734],{"className":1730},[603],[569,1732],{"className":1733,"style":1654},[607],[569,1735,1590],{"className":1736},[612]," folgt ",[569,1739,1741,1770],{"className":1740},[572],[569,1742,1744],{"className":1743},[576],[578,1745,1746],{"xmlns":580},[582,1747,1748,1767],{},[585,1749,1750,1752,1754],{},[588,1751,630],{},[703,1753,874],{},[1755,1756,1757,1765],"mfrac",{},[585,1758,1759,1761,1763],{},[588,1760,661],{},[703,1762,705],{},[707,1764,1590],{},[707,1766,1582],{},[592,1768,1769],{"encoding":594},"x = \\frac{y - 3}{2}",[569,1771,1773,1791],{"className":1772,"ariaHidden":599},[598],[569,1774,1776,1779,1782,1785,1788],{"className":1775},[603],[569,1777],{"className":1778,"style":642},[607],[569,1780,630],{"className":1781},[612,613],[569,1783],{"className":1784,"style":991},[881],[569,1786,874],{"className":1787},[995],[569,1789],{"className":1790,"style":991},[881],[569,1792,1794,1798],{"className":1793},[603],[569,1795],{"className":1796,"style":1797},[607],"height:1.2422em;vertical-align:-0.345em;",[569,1799,1801,1805,1881],{"className":1800},[612],[569,1802],{"className":1803},[963,1804],"nulldelimiter",[569,1806,1808],{"className":1807},[1755],[569,1809,1812,1872],{"className":1810},[736,1811],"vlist-t2",[569,1813,1815,1867],{"className":1814},[740],[569,1816,1819,1835,1846],{"className":1817,"style":1818},[744],"height:0.8972em;",[569,1820,1822,1826],{"style":1821},"top:-2.655em;",[569,1823],{"className":1824,"style":1825},[752],"height:3em;",[569,1827,1829],{"className":1828},[757,758,759,760],[569,1830,1832],{"className":1831},[612,760],[569,1833,1582],{"className":1834},[612,760],[569,1836,1838,1841],{"style":1837},"top:-3.23em;",[569,1839],{"className":1840,"style":1825},[752],[569,1842],{"className":1843,"style":1845},[1844],"frac-line","border-bottom-width:0.04em;",[569,1847,1849,1852],{"style":1848},"top:-3.4461em;",[569,1850],{"className":1851,"style":1825},[752],[569,1853,1855],{"className":1854},[757,758,759,760],[569,1856,1858,1861,1864],{"className":1857},[612,760],[569,1859,661],{"className":1860,"style":677},[612,613,760],[569,1862,705],{"className":1863},[1644,760],[569,1865,1590],{"className":1866},[612,760],[569,1868,1871],{"className":1869},[1870],"vlist-s","​",[569,1873,1875],{"className":1874},[740],[569,1876,1879],{"className":1877,"style":1878},[744],"height:0.345em;",[569,1880],{},[569,1882],{"className":1883},[981,1804],", nach dem Vertauschen",[569,1886,1888],{"className":1887},[832],[569,1889,1891,1933],{"className":1890},[572],[569,1892,1894],{"className":1893},[576],[578,1895,1896],{"xmlns":580,"display":841},[582,1897,1898,1930],{},[585,1899,1900,1910,1912,1914,1916,1918],{},[696,1901,1902,1904],{},[588,1903,590],{},[585,1905,1906,1908],{},[703,1907,705],{},[707,1909,709],{},[703,1911,859],{"stretchy":864},[588,1913,630],{},[703,1915,869],{"stretchy":864},[703,1917,874],{},[1755,1919,1920,1928],{},[585,1921,1922,1924,1926],{},[588,1923,630],{},[703,1925,705],{},[707,1927,1590],{},[707,1929,1582],{},[592,1931,1932],{"encoding":594},"f^{-1}(x) = \\frac{x - 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Eingeschränkt auf ",[569,2500,2502,2522],{"className":2501},[572],[569,2503,2505],{"className":2504},[576],[578,2506,2507],{"xmlns":580},[582,2508,2509,2519],{},[585,2510,2511,2513,2516],{},[588,2512,630],{},[703,2514,2515],{},"≥",[707,2517,2518],{},"0",[592,2520,2521],{"encoding":594},"x \\geq 0",[569,2523,2525,2544],{"className":2524,"ariaHidden":599},[598],[569,2526,2528,2532,2535,2538,2541],{"className":2527},[603],[569,2529],{"className":2530,"style":2531},[607],"height:0.7719em;vertical-align:-0.136em;",[569,2533,630],{"className":2534},[612,613],[569,2536],{"className":2537,"style":991},[881],[569,2539,2515],{"className":2540},[995],[569,2542],{"className":2543,"style":991},[881],[569,2545,2547,2550],{"className":2546},[603],[569,2548],{"className":2549,"style":1654},[607],[569,2551,2518],{"className":2552},[612]," ist die Umkehrfunktion 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",[569,2729,2731,2764],{"className":2730},[572],[569,2732,2734],{"className":2733},[576],[578,2735,2736],{"xmlns":580},[582,2737,2738,2761],{},[585,2739,2740,2743,2746,2748,2755,2757,2759],{},[588,2741,2742],{},"ln",[703,2744,2745],{},"⁡",[703,2747,859],{"stretchy":864},[696,2749,2750,2753],{},[588,2751,2752],{},"e",[588,2754,630],{},[703,2756,869],{"stretchy":864},[703,2758,874],{},[588,2760,630],{},[592,2762,2763],{"encoding":594},"\\ln(e^x) = x",[569,2765,2767,2822],{"className":2766,"ariaHidden":599},[598],[569,2768,2770,2773,2777,2780,2810,2813,2816,2819],{"className":2769},[603],[569,2771],{"className":2772,"style":1293},[607],[569,2774,2742],{"className":2775},[2776],"mop",[569,2778,859],{"className":2779},[963],[569,2781,2783,2786],{"className":2782},[612],[569,2784,2752],{"className":2785},[612,613],[569,2787,2789],{"className":2788},[732],[569,2790,2792],{"className":2791},[736],[569,2793,2795],{"className":2794},[740],[569,2796,2799],{"className":2797,"style":2798},[744],"height:0.6644em;",[569,2800,2801,2804],{"style":748},[569,2802],{"className":2803,"style":753},[752],[569,2805,2807],{"className":2806},[757,758,759,760],[569,2808,630],{"className":2809},[612,613,760],[569,2811,869],{"className":2812},[981],[569,2814],{"className":2815,"style":991},[881],[569,2817,874],{"className":2818},[995],[569,2820],{"className":2821,"style":991},[881],[569,2823,2825,2828],{"className":2824},[603],[569,2826],{"className":2827,"style":642},[607],[569,2829,630],{"className":2830},[612,613],[569,2832,2834,2862],{"className":2833},[572],[569,2835,2837],{"className":2836},[576],[578,2838,2839],{"xmlns":580},[582,2840,2841,2859],{},[585,2842,2843,2855,2857],{},[696,2844,2845,2847],{},[588,2846,2752],{},[585,2848,2849,2851,2853],{},[588,2850,2742],{},[703,2852,2745],{},[588,2854,630],{},[703,2856,874],{},[588,2858,630],{},[592,2860,2861],{"encoding":594},"e^{\\ln x} = x",[569,2863,2865,2928],{"className":2864,"ariaHidden":599},[598],[569,2866,2868,2872,2919,2922,2925],{"className":2867},[603],[569,2869],{"className":2870,"style":2871},[607],"height:0.8491em;",[569,2873,2875,2878],{"className":2874},[612],[569,2876,2752],{"className":2877},[612,613],[569,2879,2881],{"className":2880},[732],[569,2882,2884],{"className":2883},[736],[569,2885,2887],{"className":2886},[740],[569,2888,2890],{"className":2889,"style":2871},[744],[569,2891,2892,2895],{"style":748},[569,2893],{"className":2894,"style":753},[752],[569,2896,2898],{"className":2897},[757,758,759,760],[569,2899,2901,2912,2916],{"className":2900},[612,760],[569,2902,2904,2908],{"className":2903},[2776,760],[569,2905,2907],{"className":2906},[760],"l",[569,2909,2911],{"className":2910},[760],"n",[569,2913],{"className":2914,"style":2915},[881,760],"margin-right:0.1952em;",[569,2917,630],{"className":2918},[612,613,760],[569,2920],{"className":2921,"style":991},[881],[569,2923,874],{"className":2924},[995],[569,2926],{"className":2927,"style":991},[881],[569,2929,2931,2934],{"className":2930},[603],[569,2932],{"className":2933,"style":642},[607],[569,2935,630],{"className":2936},[612,613]," für ",[569,2939,2941,2960],{"className":2940},[572],[569,2942,2944],{"className":2943},[576],[578,2945,2946],{"xmlns":580},[582,2947,2948,2957],{},[585,2949,2950,2952,2955],{},[588,2951,630],{},[703,2953,2954],{},">",[707,2956,2518],{},[592,2958,2959],{"encoding":594},"x > 0",[569,2961,2963,2982],{"className":2962,"ariaHidden":599},[598],[569,2964,2966,2970,2973,2976,2979],{"className":2965},[603],[569,2967],{"className":2968,"style":2969},[607],"height:0.5782em;vertical-align:-0.0391em;",[569,2971,630],{"className":2972},[612,613],[569,2974],{"className":2975,"style":991},[881],[569,2977,2954],{"className":2978},[995],[569,2980],{"className":2981,"style":991},[881],[569,2983,2985,2988],{"className":2984},[603],[569,2986],{"className":2987,"style":1654},[607],[569,2989,2518],{"className":2990},[612],[560,2992,2994],{"id":2993},"typische-fehler","Typische Fehler",[2996,2997,2998,3618,3886],"ul",{},[1237,2999,3000,3068,3069,3161,3162,3372,3373,3582,3583,3617],{},[569,3001,3003,3024],{"className":3002},[572],[569,3004,3006],{"className":3005},[576],[578,3007,3008],{"xmlns":580},[582,3009,3010,3022],{},[585,3011,3012],{},[696,3013,3014,3016],{},[588,3015,590],{},[585,3017,3018,3020],{},[703,3019,705],{},[707,3021,709],{},[592,3023,712],{"encoding":594},[569,3025,3027],{"className":3026,"ariaHidden":599},[598],[569,3028,3030,3033],{"className":3029},[603],[569,3031],{"className":3032,"style":722},[607],[569,3034,3036,3039],{"className":3035},[612],[569,3037,590],{"className":3038,"style":614},[612,613],[569,3040,3042],{"className":3041},[732],[569,3043,3045],{"className":3044},[736],[569,3046,3048],{"className":3047},[740],[569,3049,3051],{"className":3050,"style":745},[744],[569,3052,3053,3056],{"style":748},[569,3054],{"className":3055,"style":753},[752],[569,3057,3059],{"className":3058},[757,758,759,760],[569,3060,3062,3065],{"className":3061},[612,760],[569,3063,705],{"className":3064},[612,760],[569,3066,709],{"className":3067},[612,760]," als Kehrwert lesen: Für ",[569,3070,3072,3101],{"className":3071},[572],[569,3073,3075],{"className":3074},[576],[578,3076,3077],{"xmlns":580},[582,3078,3079,3099],{},[585,3080,3081,3083,3085,3087,3089,3091,3093,3095,3097],{},[588,3082,590],{},[703,3084,859],{"stretchy":864},[588,3086,630],{},[703,3088,869],{"stretchy":864},[703,3090,874],{},[707,3092,1582],{},[588,3094,630],{},[703,3096,1587],{},[707,3098,1590],{},[592,3100,1593],{"encoding":594},[569,3102,3104,3131,3152],{"className":3103,"ariaHidden":599},[598],[569,3105,3107,3110,3113,3116,3119,3122,3125,3128],{"className":3106},[603],[569,3108],{"className":3109,"style":1293},[607],[569,3111,590],{"className":3112,"style":614},[612,613],[569,3114,859],{"className":3115},[963],[569,3117,630],{"className":3118},[612,613],[569,3120,869],{"className":3121},[981],[569,3123],{"className":3124,"style":991},[881],[569,3126,874],{"className":3127},[995],[569,3129],{"className":3130,"style":991},[881],[569,3132,3134,3137,3140,3143,3146,3149],{"className":3133},[603],[569,3135],{"className":3136,"style":1630},[607],[569,3138,1582],{"className":3139},[612],[569,3141,630],{"className":3142},[612,613],[569,3144],{"className":3145,"style":1640},[881],[569,3147,1587],{"className":3148},[1644],[569,3150],{"className":3151,"style":1640},[881],[569,3153,3155,3158],{"className":3154},[603],[569,3156],{"className":3157,"style":1654},[607],[569,3159,1590],{"className":3160},[612]," 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1",[569,3213,3215,3274,3363],{"className":3214,"ariaHidden":599},[598],[569,3216,3218,3221,3256,3259,3262,3265,3268,3271],{"className":3217},[603],[569,3219],{"className":3220,"style":2210},[607],[569,3222,3224,3227],{"className":3223},[612],[569,3225,590],{"className":3226,"style":614},[612,613],[569,3228,3230],{"className":3229},[732],[569,3231,3233],{"className":3232},[736],[569,3234,3236],{"className":3235},[740],[569,3237,3239],{"className":3238,"style":745},[744],[569,3240,3241,3244],{"style":748},[569,3242],{"className":3243,"style":753},[752],[569,3245,3247],{"className":3246},[757,758,759,760],[569,3248,3250,3253],{"className":3249},[612,760],[569,3251,705],{"className":3252},[612,760],[569,3254,709],{"className":3255},[612,760],[569,3257,859],{"className":3258},[963],[569,3260,3188],{"className":3261},[612],[569,3263,869],{"className":3264},[981],[569,3266],{"className":3267,"style":991},[881],[569,3269,874],{"className":3270},[995],[569,3272],{"className":3273,"style":991},[881],[569,3275,3277,3280,3354,3357,3360],{"className":3276},[603],[569,3278],{"className":3279,"style":2270},[607],[569,3281,3283,3286,3351],{"className":3282},[612],[569,3284],{"className":3285},[963,1804],[569,3287,3289],{"className":3288},[1755],[569,3290,3292,3343],{"className":3291},[736,1811],[569,3293,3295,3340],{"className":3294},[740],[569,3296,3298,3312,3320],{"className":3297,"style":2289},[744],[569,3299,3300,3303],{"style":1821},[569,3301],{"className":3302,"style":1825},[752],[569,3304,3306],{"className":3305},[757,758,759,760],[569,3307,3309],{"className":3308},[612,760],[569,3310,1582],{"className":3311},[612,760],[569,3313,3314,3317],{"style":1837},[569,3315],{"className":3316,"style":1825},[752],[569,3318],{"className":3319,"style":1845},[1844],[569,3321,3322,3325],{"style":2314},[569,3323],{"className":3324,"style":1825},[752],[569,3326,3328],{"className":3327},[757,758,759,760],[569,3329,3331,3334,3337],{"className":3330},[612,760],[569,3332,3188],{"className":3333},[612,760],[569,3335,705],{"className":3336},[1644,760],[569,3338,1590],{"className":3339},[612,760],[569,3341,1871],{"className":3342},[1870],[569,3344,3346],{"className":3345},[740],[569,3347,3349],{"className":3348,"style":1878},[744],[569,3350],{},[569,3352],{"className":3353},[981,1804],[569,3355],{"className":3356,"style":991},[881],[569,3358,874],{"className":3359},[995],[569,3361],{"className":3362,"style":991},[881],[569,3364,3366,3369],{"className":3365},[603],[569,3367],{"className":3368,"style":1654},[607],[569,3370,709],{"className":3371},[612],", aber ",[569,3374,3376,3411],{"className":3375},[572],[569,3377,3379],{"className":3378},[576],[578,3380,3381],{"xmlns":580},[582,3382,3383,3408],{},[585,3384,3385,3399,3401],{},[1755,3386,3387,3389],{},[707,3388,709],{},[585,3390,3391,3393,3395,3397],{},[588,3392,590],{},[703,3394,859],{"stretchy":864},[707,3396,3188],{},[703,3398,869],{"stretchy":864},[703,3400,874],{},[1755,3402,3403,3405],{},[707,3404,709],{},[707,3406,3407],{},"13",[592,3409,3410],{"encoding":594},"\\frac{1}{f(5)} = 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Die ",[569,3584,3586,3602],{"className":3585},[572],[569,3587,3589],{"className":3588},[576],[578,3590,3591],{"xmlns":580},[582,3592,3593,3599],{},[585,3594,3595,3597],{},[703,3596,705],{},[707,3598,709],{},[592,3600,3601],{"encoding":594},"-1",[569,3603,3605],{"className":3604,"ariaHidden":599},[598],[569,3606,3608,3611,3614],{"className":3607},[603],[569,3609],{"className":3610,"style":1630},[607],[569,3612,705],{"className":3613},[612],[569,3615,709],{"className":3616},[612]," ist hier kein Exponent.",[1237,3619,3620,3621,3161,3680,3828,3829,3857,3858,2365],{},"Eine nicht umkehrbare Funktion umkehren: Bei 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= 2^2 = 4",[569,3720,3722,3775,3819],{"className":3721,"ariaHidden":599},[598],[569,3723,3725,3728,3731,3734,3737,3766,3769,3772],{"className":3724},[603],[569,3726],{"className":3727,"style":2210},[607],[569,3729,859],{"className":3730},[963],[569,3732,705],{"className":3733},[612],[569,3735,1582],{"className":3736},[612],[569,3738,3740,3743],{"className":3739},[981],[569,3741,869],{"className":3742},[981],[569,3744,3746],{"className":3745},[732],[569,3747,3749],{"className":3748},[736],[569,3750,3752],{"className":3751},[740],[569,3753,3755],{"className":3754,"style":745},[744],[569,3756,3757,3760],{"style":748},[569,3758],{"className":3759,"style":753},[752],[569,3761,3763],{"className":3762},[757,758,759,760],[569,3764,1582],{"className":3765},[612,760],[569,3767],{"className":3768,"style":991},[881],[569,3770,874],{"className":3771},[995],[569,3773],{"className":3774,"style":991},[881],[569,3776,3778,3781,3810,3813,3816],{"className":3777},[603],[569,3779],{"className":3780,"style":745},[607],[569,3782,3784,3787],{"className":3783},[612],[569,3785,1582],{"className":3786},[612],[569,3788,3790],{"className":3789},[732],[569,3791,3793],{"className":3792},[736],[569,3794,3796],{"className":3795},[740],[569,3797,3799],{"className":3798,"style":745},[744],[569,3800,3801,3804],{"style":748},[569,3802],{"className":3803,"style":753},[752],[569,3805,3807],{"className":3806},[757,758,759,760],[569,3808,1582],{"className":3809},[612,760],[569,3811],{"className":3812,"style":991},[881],[569,3814,874],{"className":3815},[995],[569,3817],{"className":3818,"style":991},[881],[569,3820,3822,3825],{"className":3821},[603],[569,3823],{"className":3824,"style":1654},[607],[569,3826,2102],{"className":3827},[612],"; zu ",[569,3830,3832,3845],{"className":3831},[572],[569,3833,3835],{"className":3834},[576],[578,3836,3837],{"xmlns":580},[582,3838,3839,3843],{},[585,3840,3841],{},[707,3842,2102],{},[592,3844,2102],{"encoding":594},[569,3846,3848],{"className":3847,"ariaHidden":599},[598],[569,3849,3851,3854],{"className":3850},[603],[569,3852],{"className":3853,"style":1654},[607],[569,3855,2102],{"className":3856},[612]," gibt es ohne Einschränkung kein eindeutiges ",[569,3859,3861,3874],{"className":3860},[572],[569,3862,3864],{"className":3863},[576],[578,3865,3866],{"xmlns":580},[582,3867,3868,3872],{},[585,3869,3870],{},[588,3871,630],{},[592,3873,630],{"encoding":594},[569,3875,3877],{"className":3876,"ariaHidden":599},[598],[569,3878,3880,3883],{"className":3879},[603],[569,3881],{"className":3882,"style":642},[607],[569,3884,630],{"className":3885},[612,613],[1237,3887,3888,3889,1366,3917,3945],{},"Das Vertauschen von ",[569,3890,3892,3905],{"className":3891},[572],[569,3893,3895],{"className":3894},[576],[578,3896,3897],{"xmlns":580},[582,3898,3899,3903],{},[585,3900,3901],{},[588,3902,630],{},[592,3904,630],{"encoding":594},[569,3906,3908],{"className":3907,"ariaHidden":599},[598],[569,3909,3911,3914],{"className":3910},[603],[569,3912],{"className":3913,"style":642},[607],[569,3915,630],{"className":3916},[612,613],[569,3918,3920,3933],{"className":3919},[572],[569,3921,3923],{"className":3922},[576],[578,3924,3925],{"xmlns":580},[582,3926,3927,3931],{},[585,3928,3929],{},[588,3930,661],{},[592,3932,661],{"encoding":594},[569,3934,3936],{"className":3935,"ariaHidden":599},[598],[569,3937,3939,3942],{"className":3938},[603],[569,3940],{"className":3941,"style":673},[607],[569,3943,661],{"className":3944,"style":677},[612,613]," vergessen: Dann steht zwar die richtige Rechnung da, aber die Funktion ist nach der falschen Variablen benannt.",{"title":3947,"searchDepth":3948,"depth":3948,"links":3949},"",2,[3950,3951,3952],{"id":562,"depth":3948,"text":563},{"id":1554,"depth":3948,"text":1555},{"id":2993,"depth":3948,"text":2994},[3954,3956,3958,3962,3966,3968,3970,3972,3974,3976,3979],{"lhs":3955,"rhs":630},"((2*x + 3) - 3)\u002F2",{"lhs":3957,"rhs":630},"2*((x - 3)\u002F2) + 3",{"lhs":3959,"rhs":2109,"where":3960},"2*x + 3",{"x":3961},4,{"lhs":3963,"rhs":2102,"where":3964},"(x - 3)\u002F2",{"x":3965},11,{"lhs":3967,"rhs":630},"sqrt(x^2)",{"lhs":3969,"rhs":630},"sqrt(x)^2",{"lhs":3971,"rhs":630},"log(e^x)",{"lhs":3973,"rhs":630},"e^log(x)",{"lhs":3975,"rhs":709},"(5 - 3)\u002F2",{"lhs":3977,"rhs":3978},"1\u002F(2*5 + 3)","1\u002F13",{"lhs":3980,"rhs":3981},"(-2)^2","2^2","f \\text{ umkehrbar, d.h. jeder Funktionswert wird nur einmal angenommen}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Ffunctions\u002Fumkehrfunktion",[],[4045,4046,4047,4048],"log-function","natural-exponential-function","linear-function","inverse-function-derivative",{"title":548,"description":3947},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fumkehrfunktion","Die 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