invers f(x)=7\sqrt[7]{x}+5

Lösung

invers

f (x) = 7 7 x + 5

\frac{x ^{7}}{823543} - \frac{5 x ^{6}}{117649} + \frac{75 x ^{5}}{117649} - \frac{625 x ^{4}}{117649} + \frac{3125 x ^{3}}{117649} - \frac{9375 x ^{2}}{117649} + \frac{15625 x}{117649} - \frac{78125}{823543}

Schritte zur Lösung

y = 7 7 x + 5

Ersetze

x

durch

y

x = 7 7 y + 5

Löse nach

y, x = 7 7 y + 5

\frac{x ^{7}}{823543} - \frac{5 x ^{6}}{117649} + \frac{75 x ^{5}}{117649} - \frac{625 x ^{4}}{117649} + \frac{3125 x ^{3}}{117649} - \frac{9375 x ^{2}}{117649} + \frac{15625 x}{117649} - \frac{78125}{823543}

in v erse f (x) = 5 x^{\frac{5}{2}}

in v erse f (x) = - \frac{4}{3 x ^{2}} + \frac{4}{3}

in v erse f (x) = (5 - x^{3})^{\frac{1}{5}}

in v erse f (x) = \frac{4 x + 6}{5}

in v erse f (x) = x^{2} - 14 x