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Question Number 142674 by Snail last updated on 03/Jun/21

$$Iff\left(x\right)=\frac{x-3}{x+1}andh\left(x\right)=f\left(f\left(f\left(f(..2022times\left(f\left(x\right)\right))\right)\right)\right)$$$$thenh\left(1\right)=?$$

Answered by iloveisrael last updated on 04/Jun/21

$$f\left(f\left(x\right)\right)=\frac{\frac{x-3}{x+1}-3}{\frac{x-3}{x+1}+1}=\frac{x-3-3x-3}{x-3+x+1}$$$$f\left(f\left(x\right)\right)=\frac{-2x-6}{2x-2}=\frac{-x-3}{x-1}=f^{-1}\left(x\right)$$$$\text{Extra left or missing right}$$$$h\left(x\right)=x\Rightarrow h\left(1\right)=1$$

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