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Question Number 206136 by cortano21 last updated on 07/Apr/24

Answered by A5T last updated on 07/Apr/24

$$f\left(f\left(f\left(f\left(x\right)\right)\right)\right)={\left[f\left(x\right)\right]}^2-3\left[f\left(x\right)\right]+4=f(x^2-3x+4)$$$${\left[f\left(2\right)\right]}^2-3\left[f\left(2\right)\right]+4=f\left(2\right)\Rightarrow {\left[f\left(2\right)\right]}^2-4f\left(2\right)+4=0$$$${[f\left(2\right)-2]}^2=0\Rightarrow f\left(2\right)=2$$

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