f-x-1-f-x-3f-x-f-x-1-D-f-N-2023-f-1402-1-have-equation-f-x-1-solution-

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

f (x + 1) - f (x) = 3 f (x) \times f (x + 1)

D_{f} = N

2023 \times f (1402) = 1

h a v e e q u a t i o n f (x) = 1 s o l u t i o n ?

Answered by Frix last updated on 10/Dec/23

f (x + 1) = \frac{f (x)}{3 f (x) + 1}

f (0) = c

\Rightarrow

f (1) = \frac{c}{3 c + 1}

f (2) = \frac{c}{6 c + 1}

\dots

f (n) = \frac{c}{3 n c + 1}

f (1402) = \frac{1}{2023} = \frac{c}{3 \times 1402 c + 1} \Rightarrow c = - \frac{1}{2103}

f (x) = \frac{1}{3 x - 2183}

f (728) = 1

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