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Question Number 112393 by ZiYangLee last updated on 07/Sep/20

$${gf}^{-1}\left(x\right)=3x-2$$$$fg\left(x\right)=12x-8$$$$$$$$\mathrm{then}{g}^2\left(x\right)=?$$

Commented by ZiYangLee last updated on 07/Sep/20

$$\mathrm{ya}$$

Commented by john santu last updated on 07/Sep/20

$${gf}^{-1}=g\left(f^{-1}\right)?$$

Commented by kaivan.ahmadi last updated on 07/Sep/20

$${gf}^{-1}\left(fg\left(x\right)\right)={gf}^{-1}(12x-8)=3(12x-8)-2=$$$$36x-24-2=36x-26$$$$ontheotherhand$$$${gf}^{-1}\left(fg\left(x\right)\right)=\left(g\left(f^{-1}f\right)g\right)\left(x\right)=\left({gI}_{x}g\right)\left(x\right)=$$$$g^2\left(x\right)$$

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