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Question Number 190137 by mustafazaheen last updated on 28/Mar/23

$$\{\begin{array}{l}{\mathrm{fog}}^{-1}\left(\mathrm{x}\right)=3\mathrm{x}+2\\ \mathrm{gof}\left(\mathrm{x}\right)=2\mathrm{x}-1\end{array}$$$$find\mathrm{f}\left(\mathrm{x}\right)=?\mathrm{and}\mathrm{fof}\left(3\right)=?$$

Answered by 073 last updated on 28/Mar/23

$$\mathrm{f}\left(\mathrm{x}\right)={\mathrm{g}}^{-1}(2\mathrm{x}-1)$$$${\mathrm{g}}^{-1}\left(\mathrm{x}\right)=\mathrm{f}\left(\frac{\mathrm{x}+1}{2}\right)$$$$\mathrm{fof}\left(\frac{\mathrm{x}+1}{2}\right)=3\mathrm{x}+2$$$$\mathrm{fof}\left(\mathrm{x}\right)=6\mathrm{x}-1$$$$\mathrm{fof}\left(3\right)=18-1=17$$$$\mathrm{fof}\left(3\right)=17$$$$\mathrm{Math}\mathrm{lover}$$

Answered by cortano12 last updated on 28/Mar/23

$$\{\begin{array}{l}\left({\mathrm{fog}}^{-1}\right)\left(\mathrm{x}\right)=3\mathrm{x}+2\\ \left(\mathrm{gof}\right)\left(\mathrm{x}\right)=2\mathrm{x}-1\end{array}$$$$\Rightarrow \mathrm{f}\left({\mathrm{g}}^{-1}\left(\mathrm{gof}\right)\right)\left(\mathrm{x}\right)=3(2\mathrm{x}-1)+2$$$$\Rightarrow \mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=6\mathrm{x}-1$$$$\Rightarrow \mathrm{f}\left(\mathrm{f}\left(3\right)\right)=6.3-1=17$$$$$$

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