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Question Number 201681 by jabarsing last updated on 10/Dec/23

$$f(x+1)-f\left(x\right)=3f\left(x\right)\times f(x+1)$$$$D_f=N$$$$2023\times f\left(1402\right)=1$$$$haveequationf\left(x\right)=1solution?$$

Answered by Frix last updated on 10/Dec/23

$$f(x+1)=\frac{f\left(x\right)}{3f\left(x\right)+1}$$$$f\left(0\right)=c$$$$\Rightarrow$$$$f\left(1\right)=\frac{c}{3c+1}$$$$f\left(2\right)=\frac{c}{6c+1}$$$$...$$$$f\left(n\right)=\frac{c}{3nc+1}$$$$f\left(1402\right)=\frac{1}{2023}=\frac{c}{3\times 1402c+1}\Rightarrow c=-\frac{1}{2103}$$$$f\left(x\right)=\frac{1}{3x-2183}$$$$f\left(728\right)=1$$

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