Question

Functions

Answer 1

what about them?

Answer 2

@Preetha

Answer 3

\(\large \color{black}{\begin{align} & f(x)=f(x-2)-f(x-1),\ x\in \mathbb{N} \hspace{.33em}\\~\\
& f(1)=0,f(2)=1 \hspace{.33em}\\~\\
& f(10)=? \hspace{.33em}\\~\\
\end{align}}\)

Answer 4

i m looking for a short way

Answer 5

x∈N
so f(x)∈N

you can see f(x) as \[a_n\]

so now
\[a_{n}=a_{n-2}-a_{n-1}\\a_2=1\\a_1=0\\\]
charachteristic equation

\[t^2=1-t\\t^2+t-1=0\\a_n=A t_1^n +B t_2^n\]

Answer 6

find roots and apply initial condition
you will have the closed formula for it

Answer 7

i didnt understand how u found this \(t^2=1-t\)

Answer 8

nor i have studied characteristic equation

Answer 9

oh ...
i can't help you ,for fast method
sorry