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Question Number 38367 by Zuarkton last updated on 24/Jun/18

$$Iff\left(x\right)=x^3+1then{f}^{-1}\left(x\right)=?$$

Commented by rahul 19 last updated on 24/Jun/18

$${(x-1)}^{\frac{1}{3}}$$

Commented by Zuarkton last updated on 24/Jun/18

$$Solution?$$

Answered by MrW3 last updated on 24/Jun/18

$$y=f\left(x\right)=x^3+1$$$$\Rightarrow x={}^3\sqrt{y-1}$$$$\Rightarrow f^{-1}\left(x\right)={}^3\sqrt{x-1}$$

Answered by Rio Mike last updated on 25/Jun/18

$$lety=x^3+1$$$$x^3=y-1$$$$x={(y-1)}^{1/3}$$$$replacingxby{f}^{-1}\left(x\right)andybyx$$$$\Rightarrow f^{-1}\left(x\right)={(x-1)}^{1/3}$$

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