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Question Number 123987 by mnjuly1970 last updated on 29/Nov/20

$$...nicemathematics...$$$$iff\left(x\right)=x^3+xthen$$$$find{f}^{-1}\left(x\right)=?$$$$$$

Answered by MJS_new last updated on 29/Nov/20

$$y^3+y-x=0$$$$D=\frac{1}{27}+\frac{x^2}{4}>0\mathrm{\forall }x\in \mathbb{R}$$$$\Rightarrow$$$$f^{-1}\left(x\right)=\sqrt[3]{\frac{x}{2}+\frac{\sqrt{3(27x^2+4)}}{18}}-\sqrt[3]{-\frac{x}{2}+\frac{\sqrt{3(27x^2+4)}}{18}}$$

Commented by john_santu last updated on 30/Nov/20

$$Cardano$$

Commented by MJS_new last updated on 30/Nov/20

$$\mathrm{yes}$$

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