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mathmath333
 one year ago
Functions
mathmath333
 one year ago
Functions

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \color{black}{\begin{align} & f(x)=f(x2)f(x1),\ x\in \mathbb{N} \hspace{.33em}\\~\\ & f(1)=0,f(2)=1 \hspace{.33em}\\~\\ & f(10)=? \hspace{.33em}\\~\\ \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2i m looking for a short way

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1x∈N so f(x)∈N you can see f(x) as \[a_n\] so now \[a_{n}=a_{n2}a_{n1}\\a_2=1\\a_1=0\\\] charachteristic equation \[t^2=1t\\t^2+t1=0\\a_n=A t_1^n +B t_2^n\]

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1find roots and apply initial condition you will have the closed formula for it

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2i didnt understand how u found this \(t^2=1t\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2nor i have studied characteristic equation

amoodarya
 one year ago
Best ResponseYou've already chosen the best response.1oh ... i can't help you ,for fast method sorry
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