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Question Number 177688 by mathlove last updated on 08/Oct/22

$${fog}^{-1}=3x+2$$$${\left(gof\right)}_x=2x-1\stackrel{\begin{array}{c}\\ \end{array}\}{\left(fof\right)}_3=?}{}$$

Commented by cortano1 last updated on 08/Oct/22

$$\mathrm{f}\left({\mathrm{g}}^{-1}\left(\mathrm{x}\right)\right)=3\mathrm{x}+2$$$$\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=2\mathrm{x}-1$$$$\mathrm{f}\left({\mathrm{g}}^{-1}\left(\mathrm{gof}\right)\left(\mathrm{x}\right)\right)=\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=3(2\mathrm{x}-1)+2$$$$\Rightarrow \mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=6\mathrm{x}-1$$$$\Rightarrow \mathrm{f}\left(\mathrm{f}\left(3\right)\right)=17$$

Commented by mathlove last updated on 09/Oct/22

$$thanks$$

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