f-x-x-3-3x-f-1-x-

Question Number 85238 by naka3546 last updated on 20/Mar/20

f (x) = x^{3} + 3 x

f^{- 1} (x) = ?

Answered by mr W last updated on 20/Mar/20

y = x^{3} + 3 x

x^{3} + 3 x - y = 0

\Rightarrow x = \sqrt[3]{\sqrt{1 + \frac{y^{2}}{4}} + \frac{y}{2}} - \sqrt[3]{\sqrt{1 + \frac{y^{2}}{4}} - \frac{y}{2}}

\Rightarrow f^{- 1} (x) = \sqrt[3]{\sqrt{1 + \frac{x^{2}}{4}} + \frac{x}{2}} - \sqrt[3]{\sqrt{1 + \frac{x^{2}}{4}} - \frac{x}{2}}

Commented by jagoll last updated on 20/Mar/20

cardano ?

Commented by mr W last updated on 20/Mar/20

y e s

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