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Beliebt Funktionen >

f=f^9

Lösung

f = f^{9}

Lösung

f = 0, f = - \frac{2}{2} + i \frac{2}{2}, f = - \frac{2}{2} - i \frac{2}{2}, f = \frac{2}{2} + i \frac{2}{2}, f = \frac{2}{2} - i \frac{2}{2}, f = i, f = - i, f = - 1, f = 1

Schritte zur Lösung

f = f^{9}

Tausche die Seiten

f^{9} = f

Verschiebe

f

auf die linke Seite

f^{9} - f = 0

Faktorisiere

f^{9} - f : f (f^{2} + 2 f + 1) (f^{2} - 2 f + 1) (f^{2} + 1) (f + 1) (f - 1)

f (f^{2} + 2 f + 1) (f^{2} - 2 f + 1) (f^{2} + 1) (f + 1) (f - 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

f = 0 or f^{2} + 2 f + 1 = 0 or f^{2} - 2 f + 1 = 0 or f^{2} + 1 = 0 or f + 1 = 0 or f - 1 = 0

Löse

f^{2} + 2 f + 1 = 0 : f = - \frac{2}{2} + i \frac{2}{2}, f = - \frac{2}{2} - i \frac{2}{2}

Löse

f^{2} - 2 f + 1 = 0 : f = \frac{2}{2} + i \frac{2}{2}, f = \frac{2}{2} - i \frac{2}{2}

Löse

f^{2} + 1 = 0 : f = i, f = - i

Löse

f + 1 = 0 : f = - 1

Löse

f - 1 = 0 : f = 1

Die Lösungen sind

f = 0, f = - \frac{2}{2} + i \frac{2}{2}, f = - \frac{2}{2} - i \frac{2}{2}, f = \frac{2}{2} + i \frac{2}{2}, f = \frac{2}{2} - i \frac{2}{2}, f = i, f = - i, f = - 1, f = 1

Graph

Beliebte Beispiele

f (x) = x^{7}

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f (x) = 3 x - 8

f (x) = 3 x + 8