BdMO 2020 Regional Higher Secondary P8
f f(x)=3x-2, then what is the value of x in the following equation? x=f(f(f(...f(x)...))) [2020 times]
- Anindya Biswas
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Re: BdMO 2020 Regional Higher Secondary P8
Let's define $g$ such that $g(x)=f(f(x))$. Let's denote $\underbrace{g(g(\dots g(x)\dots))}_{n}$ by $g^n(x)$.
We can apply induction to get $g^n(x)=3^nx-3^n+1$.
Given,
$g^{1010}(x)=3^{1010}x-3^{1010}+1=x\Rightarrow \boxed{x=1}$
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