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Question Number 176850 by Ar Brandon last updated on 27/Sep/22

$$f\left(x\right)=2(x-1)$$$$\underset{50\mathrm{times}}{\underbrace{(fofo...of)}}\left(x\right)=?$$

Answered by mr W last updated on 27/Sep/22

$$f\left(x\right)=2x-2$$$$f\left(f\left(x\right)\right)=2(2x-2)-2=2^{2}x-(2^2+2)$$$$generally$$$$f\left(f\left(f(...f\left(x\right))\right)\right)=2^{n}x-(2^n+2^{n-1}+...+2^2+2)$$$$\underset{ntimes}{f\left(f\left(f(...f\left(x\right))\right)\right)}=2^{n}x-2^{n+1}+2$$

Commented by Ar Brandon last updated on 27/Sep/22

Thank you, Sir!

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