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Question Number 119808 by Khalmohmmad last updated on 27/Oct/20

$$f^{-1}\left(x\right)=3x^2+2x$$$$f\left(8\right)=?$$

Answered by Ar Brandon last updated on 27/Oct/20

$$f^{-1}\left(\mathrm{x}\right)={3\mathrm{x}}^2+2\mathrm{x}\Rightarrow f({3\mathrm{x}}^2+2\mathrm{x})=\mathrm{x}$$$$\mathrm{We}\mathrm{can}\mathrm{notice}\mathrm{that}\mathrm{for}\mathrm{x}=-2,\mathrm{f}\left(8\right)=-2$$

Answered by Dwaipayan Shikari last updated on 27/Oct/20

$$f^{-1}\left(x\right)=(3x^2+2x)$$$$f(3x^2+2x)=x$$$$3x^2+2x=8$$$$3x^2+2x-8=0\Rightarrow x=\frac{-2\pm \sqrt{4+96}}{6}=-2or\frac{4}{3}$$$$So$$$$f\left(8\right)=-2orf\left(8\right)=\frac{4}{3}$$

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