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Question Number 186870 by 073 last updated on 11/Feb/23

Commented by 073 last updated on 11/Feb/23

$$\mathrm{solution}\mathrm{please}??$$

Answered by Ar Brandon last updated on 11/Feb/23

$$\{\begin{array}{ll}f\mathrm{o}{g}^{-1}\left(x\right)=3x+2& ...\left(i\right)\\ g\mathrm{o}f\left(x\right)=2x-1& ...\left(ii\right)\end{array}$$$$\left(ii\right)\Rightarrow f\left(x\right)=g^{-1}(2x-1)$$$$\Rightarrow f\left(3\right)=g^{-1}\left(5\right)$$$$\Rightarrow f\mathrm{o}f\left(3\right)=f\mathrm{o}{g}^{-1}\left(5\right)=3\left(5\right)+2=17$$

Commented by AROUNAMoussa last updated on 12/Feb/23

Toutes mes excuses. C'était une erreur de manipulation

Commented by ARUNG_Brandon_MBU last updated on 12/Feb/23

Pas de quoi, l'ami.

Answered by ARUNG_Brandon_MBU last updated on 11/Feb/23

$$\{\begin{array}{ll}f\mathrm{o}{g}^{-1}\left(x\right)=3x+2& ...\left(i\right)\\ g\mathrm{o}f\left(x\right)=2x-1& ...\left(ii\right)\end{array}$$$$\left(ii\right)\Rightarrow f\left(x\right)=g^{-1}(2x-1)$$$$\Rightarrow g^{-1}\left(x\right)=f\left(\frac{x+1}{2}\right)...\left(iii\right)$$$$\left(iii\right)\mathrm{in}\left(i\right)\Rightarrow f\mathrm{o}f\left(\frac{x+1}{2}\right)=3x+2$$$$\Rightarrow f\mathrm{o}f\left(x\right)=6x-1$$$$\Rightarrow f\left(3\right)=6\left(3\right)-1=17$$

Answered by aba last updated on 11/Feb/23

$$$$$$fof\left(3\right)=f\left(f\left(3\right)\right)=f\left(g^{-1}\left(g\left(f\left(3\right)\right)\right)\right)=f\left(g^{-1}\left(5\right)\right)=3\times 5+2=17$$

Answered by horsebrand11 last updated on 12/Feb/23

$$\{\begin{array}{l}f\left(g^{-1}\left(x\right)\right)=3x+2\\ g\left(f\left(x\right)\right)=2x-1\end{array}$$$$\Rightarrow g^{-1}\left(x\right)=f^{-1}(3x+2)$$$$\Rightarrow f\left(x\right)=g^{-1}(2x-1)$$$$\Rightarrow f\left(f\left(x\right)\right)=f\left(g^{-1}(2x-1)\right)$$$$\Rightarrow f\left(f\left(3\right)\right)=f\left(g^{-1}\left(5\right)\right)$$$$\Rightarrow f\left(f\left(3\right)\right)=3.5+2=17$$

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